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搜索: a321091-编号:a321091
    排序:关联|参考文献||被改进的|创建     格式:长的|短的|数据
形态0->011,1->001的不动点。
+10
12
0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1
抵消
1
配方奶粉
a(3k-2)=0,a(3k-1)=1-a(k),a(3G)=1,k>=1,a(0)=0。
例子
0->011->011001001->...
数学
t=嵌套[扁平[#/.{0->{0,1,1},1->{0,0,1}}]&,{0},5](*A189706号*)
f[n]:=t[[n]]
压扁[位置[t,0]](*A189707号*)
压扁[位置[t,1]](*A189708号*)
s[n_]:=和[f[i],{i,1,n}];s[0]=0;
表[s[n],{n,1,120}](*A189709号*)
黄体脂酮素
(PARI)a(n)=n--;我的(ret=0);而([n,r]=divrem(n,3);r==1,ret++);(ret+r>>1)%2\\凯文·莱德2021年6月2日
交叉参考
关键词
非n
作者
克拉克·金伯利2011年4月25日
状态
经核准的
满足连分式关系的序列{a(n),n>=0}:如果z=[a(0)+1;a(1)+1,a(2)+1,α(3)+1,…,a(n”+1,…],则3*z=[a(0)+9;a(l)+11,a(2+11,α(3+11,…,α(n)+11…]。
+10
11
2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1
抵消
0,1
评论
a(n)=2-A321100型(n) 对于n>=0。
a(3*n+1)=A189706号(n+1),对于n>=0。
A321091型(n) =a(n)+1,对于n>=1。
A321093型(n) 当n>=1时,=2*a(n)+1。
A321095型(n) 当n>=1时,=3*a(n)+1。
A321097型(n) =4*a(n)+1,对于n>=1。
链接
配方奶粉
连续分数关系-此序列{a(n),n>=0}满足:
(1) 如果X(k,n)=[k*a(0)+n,
则(n^2+k*n+1)*X(k,n)=[k*a(0)+m-k-n;k*a。
(2) 如果y(n)=[a(0)+n;a(1)+n,a(2)+n、a(3)+n…]
则(n^2+n+1)*y(n)=[a(0)+m-n-1;a(1)+m,a(2)+m、a(3)+m…],其中m=n^3+3*n^2+5*n+2,对于n>=0(注意n=0时的特殊情况)。
(3) 如果z(n)=[n*a(0)+1;n*a(1)+1,n*a(2)+1,n*a(3)+1,…],
则(n+2)*z(n)=[n*a(0)+m-n-1;n*a。
术语公式:对于n>=0,
(1) a(3*n)=2,
(2) a(3*n+2)=1-a(3*n+1),
(3) a(9*n+1)=0,
(4) a(9*n+7)=1,
(5) a(9*n+4)=1-a(3*n+1)。
例子
续馏分性质图1。
定义y(n)=[a(0)+n;a(1)+n,a(2)+n、a(3)+n…]
则(n^2+n+1)*y(n)=[a(0)+m-n-1;a(1)+m,a(2)+m、a(3)+m…],其中m=n^3+3*n^2+5*n+2,对于n>=0(注意n=0时的特殊情况)。
常数y(n)和初始n的相应连分式的示例如下。
案例n=0。
y(0)=3.43303149449604686065826526329327018056861743523717776168。。。
允许连分母为零,
y(0)=[2;0,1,2,1,0,2,0,0,1、2,0…,a(n)+0,…];
y(0)的简单连分式展开将其重写为
y(0)=[3;2,3,4,3,2,4,2,2,3、4,2…,a(n)+2,…]。
案例n=1。
y(1)=3.6967432859700279090379713506148996959668903498266397449760。。。
y(1)=[3;1,2,3,2,1,3,1,1,2,
3*y(1)=[11;11,12,13,12,11,13,12,11,13,…,a(n)+11,…]。
案例n=2。
y(2)=4.43303149449604860658265263299327018056861743523717776168。。。
y(2)=[4;2,3,4,3,2,4,2,2,3,
7*y(2)=[31;32,33,34,33,32,34,33,32,34…,a(n)+32,…]。
案例n=3。
y(3)=5.30877551945535750122355554493187782342126930062870320137262。。。
y(3)=[5;3、4、5、4、3、5、四、三、五、三、四、五、3……,a(n)+3,…],
13*y(3)=[69;71,72,73,72,71,73,72,71,73…,a(n)+71,…]。
案例n=4。
y(4)=6.238450584480066114628834113782413167423795477181191240204。。。
y(4)=[6;4、5、6、5、4、6、五、四、六、四、五、六、4……,a(n)+4,…],
21*y(4)=[131;134135,136135,135,134136135,…,a(n)+134,…]。
等。
续馏分性质图2。
定义z(n)=[n*a(0)+1;n*a,
则(n+2)*z(n)=[n*a(0)+m-n-1;n*a;
常数z(n)和初始n的相应连分式的示例如下。
情况n=0。
z(0)=1.61803398874989482045868343…=(1+平方(5))/2;
z(0)=[1;1,1,1,1,1,1,1,1,1,1,1,1,…,0*a(n)+1,…];
2*z(0)=[3;4,4,4。
案例n=1。
z(1)=3.69674328597002790903797135061489969596689034(A321092型- 1)
z(1)=[3;1,2,3,2,1,3,1,1,2;
3*z(1)=[11;11,12,13,12,11,13,12,11,13,…,1*a(n)+11,…]。
案例n=2。
z(2)=5.761342189260057700977872181649926352515102(A321094型- 1)
z(2)=[5;1,3,5,3,1,5,1,1,3;
4*z(2)=[23;22,24,26,24,22,26,24,22,26…,2*a(n)+22,…]。
案例n=3。
z(3)=7.805401757688663373476939995437639876411562871(A321096型- 1)
z(3)=[7;1,4,7,4,1,7,4,1,7,1,…,3*a(n)+1,…];
5*z(3)=[39;37,40,43,40,37,43,40,37,43…,3*a(n)+37,…]。
案例n=4。
z(4)=9.836308638532504943187035876427127876597685985953(A321098型- 1)
z(4)=[9;1,5,9,5,1,9,5,1,9,1,5,9,1…,4*a(n)+1,…];
6*z(4)=[59;56,60,64,60,56,64,60,56,64…,4*a(n)+56,…]。
等。
扩展条款。
该序列的最初1020项如下。
A=[2,0,1,2,1,0,2,1,1,0,0,2,0,1,0,12,0,12,1,0,1,1,0,1,0,1,
2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,
2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,
2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,
2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,
2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,
2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,
2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,
2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,
2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,
2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,
2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,
2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,
2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,
2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,
2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,
2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,
2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,
2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,
2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,
2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,
2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,
2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,
2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,
2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,
2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,
2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,
2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,
2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,
2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,
2,0,1,2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,
2,0,1,2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,
2,1,0,2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,0,1,2,1,0,
2,0,1,2,0,1,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1,2,1,0,2,1,0,2,0,1, ...].
...
黄体脂酮素
(PARI)/*生成超过5000个术语*/
{CF=[4];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,10));z=(1/3)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=0200,打印1(CF[n+1]-1-0^n,“,”)
(PARI)/*使用单个术语的公式*/
{a(n)=如果(n%3==0,2,
如果(n%3==2,1-a(n-1),
如果(n%9==1,0,
如果(n%9==7,1,
如果(n%9==4,1-a((n-1)/3)))}
对于(n=0200,打印1(a(n),“,”)
关键词
非n
作者
保罗·D·汉纳2018年10月27日
扩展
修订了示例和评论部分-保罗·D·汉纳2018年11月3日
状态
经核准的
常数z的十进制展开式满足:CF(3*z,n)=CF(z,n。
+10
9
4, 6, 9, 6, 7, 4, 3, 2, 8, 5, 9, 7, 0, 0, 2, 7, 9, 0, 9, 0, 3, 7, 9, 7, 1, 3, 5, 0, 6, 1, 4, 8, 9, 9, 6, 9, 5, 9, 6, 7, 6, 8, 9, 0, 3, 4, 9, 8, 2, 6, 6, 3, 9, 7, 4, 4, 9, 7, 6, 0, 6, 5, 8, 7, 6, 8, 9, 4, 9, 3, 0, 1, 8, 0, 5, 9, 9, 4, 9, 8, 2, 2, 7, 4, 6, 7, 9, 3, 8, 7, 8, 8, 4, 5, 2, 6, 6, 8, 7, 6, 6, 7, 3, 5, 5, 4, 3, 3, 7, 3, 7, 9, 1, 7, 9, 7, 2, 8, 0, 8, 7, 7, 1, 0, 8, 6, 8, 2, 2, 0, 9, 5, 7, 9, 0, 8, 6, 6, 2, 6, 1, 3, 6, 1, 4, 0, 3, 2, 7, 9, 8, 3, 3, 3, 8, 8, 4, 0, 5, 7, 2, 7, 5, 2, 0, 0, 8, 9, 1, 3, 3, 8, 2, 5, 0, 6, 5, 1, 0, 4, 5, 5, 3, 0, 6, 3, 8, 3, 3, 4, 7, 1, 8, 5, 7, 2, 3, 6, 7, 8, 1
抵消
1,1
链接
保罗·D·汉纳,n=1..7000时的n,a(n)表
例子
此常数z的十进制展开式开始于:
z=4.6967432859700279090379713506148996959668903498266。。。
z的简单连分式展开开始:
z=[4;1,2,3,2,1,3,1,2。。。,A321091型(n) ,…];
这样,3*z的简单连分式展开就开始了:
3*z=[14;11,12,13,12,11,13,12,11,13,11,12。。。,A321091型(n) +10,…]。
扩展条款。
z的十进制展开式中的前1000位是
z=4.6967432859700279090379713506148996959668903498266\
39744976065876894930180599498227467938788452668766\
73554337379179728087710868220957908662613614032798\
33388405727520089133825065104553063833471857236781\
30005222692602670820049366351838443544785254486817\
36713432024147916330132466297271088195927148747751\
61081134504127224293197514421215072180791056995531\
25282254039576642227973626045065085745006810232418\
31151864601858865871496634133860069172907530299184\
80599130262819282015136761682297696200354791299160\
72099154048193374507277756176907149849150248588944\
75702959853076891940422757945105365738782828309624\
89182729519410181321396021772327752921026193693551\
52235778358918181495624102484144418903334090227672\
68450214362152729231740655406007216125545132538964\
63321922981643984915752295515263408732183582572996\
74985150593020685391286450747231245540741605404683\
64053241113305130300450809189365250050022411738651\
75283281124343007394094179023437577924273245108697\
96469643376214173186511094645179990191104328112759...
...
z的连分数的最初1020项是
Z=[4;1,2,3,2,1,3,2,2,1,3,1,3,1,2,3,1,2,3,2,3,3,12,3,12,3,
2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,
2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,
1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,
1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,
2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,
1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,
1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,
2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,
1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,
2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,
2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,
1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,
2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,
2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,
1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,
1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,
2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,
1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,
2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,
2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,
1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,
1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,
2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,
1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,
1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,
2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,
1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,
2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,
2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,
1,2,3,1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,
1,2,3,2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,
2,1,3,1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,
1,2,3,1,2,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3,2,1,3,2,1,3,1,2,3, ...].
上述条款有规律吗?
...
生成方法。
从CF=[4]开始,然后重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,10));
z=(1/3)*M[1,1]/M[2,1];CF=控制(z)}
该方法可以如下所示。
z0=[4]=4;
z1=(1/3)*[14]=[4;1,2]=14/3;
z2=(1/3)*[14;11,12]=[4,1,2,3,2,1,3,3]=1874/399;
z3=(1/3)*[14;11,12,13,12,11,13,13]=[4;1,2,3,2,1,3,1,2、3,1、2、3、2、1、1、2;
z4=(1/3)*[14;11,12,13,12,11,13第二、三、一、二、三,二、一、三、二、二、三、二、一,三、二,一,四] = 254413274852180460063336/54168017999228580539039; ...
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成超过3600位数字*/
{CF=[4];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,10));z=(1/3)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=1200,打印1(楼层(10^(n-1)*z)%10,“,”)
关键词
非n,欺骗
作者
保罗·D·汉纳2018年10月27日
状态
经核准的
常数z的连续分式展开式满足:CF(4*z,n)=CF(z,n。
+10
9
6, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 3, 1, 5, 1, 3
抵消
0,1
配方奶粉
术语公式:
(1) a(0)=6,
(2) 当n>=1时,a(3*n)=5,
(3) 当n>=0时,a(3*n+2)=4-a(3xn+1),
(4) 当n>=0时,a(9*n+1)=1,
(5) 当n>=0时,a(9*n+7)=3,
(6) 对于n>=0,a(9*n+4)=4-a(3*n+1)。
a(3*n+1)=2*A189706号(n+1)+1表示n>=0。
a(n)=2*A321090型(n) n>=1时为+1,其中a(0)=6。
a(n)=A321091型(n)+A321090型(n) ,对于n>=0。
a(n)=A321095型(n)-A321090型(n) ,对于n>=0。
a(n)=A321097型(n) -2个*A321090型(n) ,对于n>=0。
例子
这个常数z的十进制展开开始于:
z=6.76134218926005257700977872218164992635251510297623。。。
z的简单连分式展开开始:
z=[6;1,3,5,3,1,5,1,3;
这样,4*z的简单连分式展开就开始了:
4*z=[27;22、24、26、24、22、26、二十四、二十二、二十六、二十二、二十二、二十四……,a(n)+21,……]。
扩展条款。
z的连分数的最初1020项是
z=[6;1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,5,1,3,5,
3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5, ...].
...
z的十进制展开式中的前1000位是
z=6.76134218926005257700977872218164992635251510297623\
82400543083129376225709036432953076227076440718046\
31453442451274796099781430687357859993593539615424\
85162251478631501261337528918395764663363544002143\
30566359813785491386584191187803105986019925125817\
32384559737235970178404167070340277684175375836022\
44216229551462644458639369128033581124838287016422\
22465666402121115108802903360423241018391788636516\
34399014131667135507041306777557247262858680853566\
90766431107666031620853273656348374218315881851585\
44479630341871788962324209888156077547855028352382\
55925436674100345760249501114992870759647092383954\
96007641595484979939448371742959430380908428799273\
24364811976473376482587750783735175570880836352529\
00570146062437832931408193409264288195544895081069\
61581071442858044513706835327745695285899243308879\
49562004677663100500730098181693102336025369092373\
55940511090331284958638975881509935173849203422329\
94160267792889652591286734230036989339097946760406\
04381955878548467565031395792149142079025146844422...
...
生成方法。
从CF=[6]开始,然后重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,21));
z=(1/4)*M[1,1]/M[2,1];CF=控制(z)}
该方法可以如下所示。
z0=[6]=6;
z1=(1/4)*[27]=[6];1,3]=27/4;
z2=(1/4)*[27;22,24]=[6;1,3,5,3,1,5,4]=14307/2116;
z3=(1/4)*[27;22,24,26,24,22,26,25]=[6;1,3,5,3,1,5,1,3,5,1,3,5,1,3,5,3,1,5,1,3,6]=32184125853/4760020267;
z4=(1/4)*[27;22,24,26,24,24,22,26,24,22,22,24第三、五、一、三、五、三、一、五、一三五、三、一五三六条] = 668028962666848193442388706037/98801235607919425997683216483 ; ...
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成5000多个术语*/
{CF=[6];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,21));z=(1/4)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=0200,打印1(CF[n+1],“,”)
关键词
非n,cofr公司
作者
保罗·D·汉纳2018年10月28日
状态
经核准的
常数z的连续分式展开式满足:CF(5*z,n)=CF(z,n。
+10
9
8, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 1, 4, 7, 4, 1, 7, 1, 4, 7, 4, 1, 7, 4, 1, 7, 1, 4
抵消
0,1
配方奶粉
术语公式:
(1) a(0)=8,
(2) 当n>=1时,a(3*n)=7,
(3) 当n>=0时,a(3*n+2)=5-a(3xn+1),
(4) 当n>=0时,a(9*n+1)=1,
(5) 当n>=0时,a(9*n+7)=4,
(6) 当n>=0时,a(9*n+4)=5-a(3*n+1)。
a(3*n+1)=3*A189706号(n+1)+1表示n>=0。
a(n)=3*A321090型(n) n>=1时+1,a(0)=8。
a(n)=A321091型(n) +2个*A321090型(n) ,对于n>=0。
a(n)=A321093型(n)+A321090型(n) ,对于n>=0。
a(n)=A321097型(n)-A321090型(n) ,对于n>=0。
例子
此常数z的十进制展开式开始于:
z=8.8054017576886633734769399543763987641156287148453。。。
z的简单连分式展开开始:
z=[8;1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,…,a(n),…];
这样,5*z的简单连分式展开就开始了:
5*z=[44;37、40、43、40、37、43、四十、37、四十三、三十七、三十七……,a(n)+36,…]。
扩展条款。
z的连续部分的初始1020项是
z=[8;1,4,7,4,1,7,4-1,7,1,4,7,14,71,4,4,4,17,4,1,4,7,
4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7, ...].
...
z的十进制展开式中的前1000位是
z=8.80540175768866337347693999543763987641156287148453\
81468516943758900177466965168383790121108844505757\
17187999454407348106496636159427234274709665063530\
50935777205767852706781920879673120741864445658376\
11976420857048526287399704761091708055469240672330\
48700326462058452646355562520962867414041721519998\
23160265836475138977655743106219535120079474624210\
99859736180993210725127756524124066610420161356552\
06399576189405297872838825683944974598313320897473\
82753910120167655227857213444857908106596044697304\
03731161925824151533224356077992140610806046874738\
76664918873754737673637688749508970659125480247854\
23148383885317039738394794978662476138806965606055\
89270492560115659978879195004407252000769277753763\
08004863113948791353859078952125599689193183276991\
65636567095719857927702210317282103234986565300353\
38502840972838489688713570280513772584527070132759\
37605094965136681249812588515170458336825974959207\
93310692922707508597239859725358109680410147516880\
36970398236866976270861217620395537245456726267033...
...
生成方法。
从CF=[8]开始,然后重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,36));
z=(1/5)*M[1,1]/M[2,1];CF=控制(z)}
该方法可以如下所示。
z0=[8]=8;
z1=(1/5)*[44]=[8;1,4]=44/5;
z2=(1/5)*[44;37,40]=[8;1,4,7,4,1,7,5]=65204/7405;
z3=(1/5)*[44;37,40,43,40,37,43,41]=[8;1,4,7,4,1,7,1,4、7,1、4、7、1、4,7、4、1、7、4,8]=1467584898352/166668703909;
z4=(1/5)*[44;37,40,43,40,37,43,40,37,43第4、7、1、4、7和4、1、7和1、4和7、4和1、7、4、1和8] = 38573876143771692243421005778572392/4380705980858842541559248009960149 ; ...
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成超过5000个术语*/
{CF=[8];对于(i=1,8,M=contfracpnqn(CF+矢量(#CF,i,36));z=(1/5)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=0200,打印1(CF[n+1],“,”)
关键词
非n,cofr公司
作者
保罗·D·汉纳2018年10月28日
状态
经核准的
常数z的连续分式展开式满足:CF(6*z,n)=CF(z,n。
+10
9
10, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 1, 5, 9, 5, 1, 9, 1, 5, 9, 5, 1, 9, 5, 1, 9, 1, 5
抵消
0,1
配方奶粉
术语公式:
(1) a(0)=10,
(2) 当n>=1时,a(3*n)=9,
(3) 当n>=0时,a(3*n+2)=6-a(3xn+1),
(4) 当n>=0时,a(9*n+1)=1,
(5) 当n>=0时,a(9*n+7)=5,
(6) 当n>=0时,a(9*n+4)=6-a(3*n+1)。
a(3*n+1)=4*A189706号(n+1)+1表示n>=0。
a(n)=4*A321090型(n) n>=1时+1,a(0)=10。
a(n)=A321091型(n) +3个*A321090型(n) ,对于n>=0。
a(n)=A321093型(n) +2个*A321090型(n) ,对于n>=0。
a(n)=A321095型(n)+A321090型(n) ,对于n>=0。
例子
此常数z的十进制展开式开始于:
z=10.8363086385325049431870358764271278765976859589534931。。。
z的简单连分式展开开始:
z=[10;1,5,9,5,1,9,5,1,9,1,5,9,…,a(n),…];
这样,6*z的简单连分式展开就开始了:
6*z=[65;56、60、64、60、56、64、六十、五十六、64、56、60……,a(n)+55,…]。
扩展条款。
z的连续部分的初始1020项是
z=[10;1,5,9,5,1,9,5A,1,9,1,5,9,15,95,1,5,10,9,10,5,15,9,
5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9, ...].
...
z的十进制展开式中的前1000位是
z=10.83630863853250494318703587642712787659768595895349311\
73840509756931960001734110072237735215798152265637\
46033548966251275029451235255917154869550414547346\
45601898326659069509029896766448634581870902999261\
78291099037993947368425232025742840508201019811150\
20208289541868116590985746685817208034834182741861\
61586263073936595659616093596727391439370392218179\
08547782927594504604528661115974783060857978290729\
53554586787471663938331763610007750862560295292956\
22583160832720034539915220107654291931753328805663\
44405451280922502018454665640681719991329902449206\
06333718948414803434770198192597675071144159105469\
40129387536502210902718153383173369508615022733071\
21561771111264471719424048701509094587624798702003\
98051339274318126056502629341701820569809346581703\
17900710636878987844980734936343020769115171474588\
61969660741202379814909712010859009313616125172084\
48790047790048120552938902316397984428482656427316\
35549261064509815824229787948467548551187722067240\
97844304015886508690953002055508602378218606168521...
...
生成方法。
从CF=[10]开始,然后重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,55));
z=(1/6)*M[1,1]/M[2,1];CF=控制(z)}
该方法可以如下所示。
z0=[10]=10;
z1=(1/6)*[65]=[10;1,5]=65/6;
z2=(1/6)*[65;56,60]=[10;1,5,9,5,1,9,6]=218525/20166;
z3=(1/6)*[65;56、60、64、60、56、64、61]=[10;1、5、9、1、9、9、1,5、9,1、5,9、5,1、9,5、1,9、1,5、10]=30617277049665/2825434201901;
z4=(1/6)*[65;56,60,64,60,56,64,6056,56,56第五、九、一、五、九、五、一、九、一五、九五、五、一九、一十条] = 235326213809918755668077578309692661245/21716455451732827969266335806481498321 ;
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成超过5000个术语*/
{CF=[10];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,55));z=(1/6)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=0200,打印1(CF[n+1],“,”)
关键词
非n,cofr公司
作者
保罗·D·汉纳,2018年10月28日
状态
经核准的
常数z的十进制展开式满足:CF(4*z,n)=CF(z,n。
+10
8
6, 7, 6, 1, 3, 4, 2, 1, 8, 9, 2, 6, 0, 0, 5, 2, 5, 7, 7, 0, 0, 9, 7, 7, 8, 7, 2, 2, 1, 8, 1, 6, 4, 9, 9, 2, 6, 3, 5, 2, 5, 1, 5, 1, 0, 2, 9, 7, 6, 2, 3, 8, 2, 4, 0, 0, 5, 4, 3, 3, 3, 6, 5, 6, 0, 3, 3, 9, 3, 1, 4, 6, 7, 6, 9, 0, 0, 4, 3, 1, 7, 5, 0, 5, 5, 8, 4, 3, 9, 3, 5, 4, 2, 7, 0, 8, 5, 9, 2, 3, 5, 9, 2, 2, 7, 8, 6, 9, 0, 3, 4, 1, 1, 6, 1, 5, 4, 2, 0, 9, 6, 7, 6, 6, 6, 3, 7, 5, 7, 9, 8, 5, 3, 1, 7, 7, 3, 6, 9, 3, 4, 3, 5, 1, 9, 0, 0, 7, 8, 1, 2, 0, 3, 9
抵消
1,1
例子
此常数z的十进制展开式开始于:
z=6.76134218926005257700977872218164992635251510297623。。。
z的简单连分式展开开始:
z=[6;1、3、5、3、1、5、1、3。。。,A321093型(n) ,…];
这样,4*z的简单连分式展开就开始了:
4*z=[27;22、24、26、24、22、26、二十四、二十二、二十六、二十二、二十二、二十四。。。,A321093型(n) +21,…]。
扩展条款。
z的十进制展开式中的前1000位是
z=6.76134218926005257700977872218164992635251510297623\
82400543083129376225709036432953076227076440718046\
31453442451274796099781430687357859993593539615424\
85162251478631501261337528918395764663363544002143\
30566359813785491386584191187803105986019925125817\
32384559737235970178404167070340277684175375836022\
44216229551462644458639369128033581124838287016422\
22465666402121115108802903360423241018391788636516\
34399014131667135507041306777557247262858680853566\
90766431107666031620853273656348374218315881851585\
44479630341871788962324209888156077547855028352382\
55925436674100345760249501114992870759647092383954\
96007641595484979939448371742959430380908428799273\
24364811976473376482587750783735175570880836352529\
00570146062437832931408193409264288195544895081069\
61581071442858044513706835327745695285899243308879\
49562004677663100500730098181693102336025369092373\
55940511090331284958638975881509935173849203422329\
94160267792889652591286734230036989339097946760406\
04381955878548467565031395792149142079025146844422...
...
z的连分数的最初1020项是
z=[6;1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,5,1,3,5,
3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,
3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,
1,3,5,3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,
3,1,5,1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,1,3,5,3,1,5,
1,3,5,1,3,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5,3,1,5,3,1,5,1,3,5, ...].
...
生成方法。
从CF=[6]开始,重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,21));
z=(1/4)*M[1,1]/M[2,1];CF=控制(z)}
这种方法可以说明如下。
z0=[6]=6;
z1=(1/4)*[27]=[6;1,3]=27/4;
z2=(1/4)*[27;22,24]=[6;1,3,5,3,1,5,4]=14307/2116;
z3=(1/4)*[27;22,24,26,24,22,26,25]=[6;1,3,5,3,1,5,1,3;
z4=(1/4)*[27;22,24,26,24,24,22,26,24,22,22,24第三、五、一、三、五、三、一、五、一三五、三、一五三六条] = 668028962666848193442388706037/98801235607919425997683216483; ...
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成超过4600位数字*/
{CF=[6];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,21));z=(1/4)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=1200,打印1(楼层(10^(n-1)*z)%10,“,”)
关键词
非n,欺骗
作者
保罗·D·汉纳2018年10月28日
状态
经核准的
常数z的十进制展开式满足:CF(5*z,n)=CF(z,n。
+10
8
8, 8, 0, 5, 4, 0, 1, 7, 5, 7, 6, 8, 8, 6, 6, 3, 3, 7, 3, 4, 7, 6, 9, 3, 9, 9, 9, 5, 4, 3, 7, 6, 3, 9, 8, 7, 6, 4, 1, 1, 5, 6, 2, 8, 7, 1, 4, 8, 4, 5, 3, 8, 1, 4, 6, 8, 5, 1, 6, 9, 4, 3, 7, 5, 8, 9, 0, 0, 1, 7, 7, 4, 6, 6, 9, 6, 5, 1, 6, 8, 3, 8, 3, 7, 9, 0, 1, 2, 1, 1, 0, 8, 8, 4, 4, 5, 0, 5, 7, 5, 7, 1, 7, 1, 8, 7, 9, 9, 9, 4, 5, 4, 4, 0, 7, 3, 4, 8, 1, 0, 6, 4, 9, 6, 6, 3, 6, 1, 5, 9, 4, 2, 7, 2, 3, 4, 2, 7, 4, 7, 0, 9, 6, 6, 5, 0, 6, 3, 5, 3, 0, 5, 0, 9, 3, 5, 7, 7, 7, 2, 0, 5, 7, 6, 7, 8, 5, 2
抵消
1,1
例子
此常数z的十进制展开式开始于:
z=8.80540175768866337347693999543763987641156287148453。。。
z的简单连分式展开开始:
z=[8;1、4、7、4、1、7、4,1、7、1、4,7,1、4,7。。。,A321095型(n) ,…];
这样,5*z的简单连分式展开就开始了:
5*z=[44;37、40、43、40、37、43、四十、37、四十三、三十七。。。,A321095型(n) +36,…]。
扩展条款。
z的十进制扩展中的最初1000位数字是
z=8.80540175768866337347693999543763987641156287148453\
81468516943758900177466965168383790121108844505757\
17187999454407348106496636159427234274709665063530\
50935777205767852706781920879673120741864445658376\
11976420857048526287399704761091708055469240672330\
48700326462058452646355562520962867414041721519998\
23160265836475138977655743106219535120079474624210\
99859736180993210725127756524124066610420161356552\
06399576189405297872838825683944974598313320897473\
82753910120167655227857213444857908106596044697304\
03731161925824151533224356077992140610806046874738\
76664918873754737673637688749508970659125480247854\
23148383885317039738394794978662476138806965606055\
89270492560115659978879195004407252000769277753763\
08004863113948791353859078952125599689193183276991\
65636567095719857927702210317282103234986565300353\
38502840972838489688713570280513772584527070132759\
37605094965136681249812588515170458336825974959207\
93310692922707508597239859725358109680410147516880\
36970398236866976270861217620395537245456726267033...
...
z的连分数的最初1020项是
z=[8;1,4,7,4,1,7,4-1,7,1,4,7,14,71,4,4,4,17,4,1,4,7,
4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,
4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,
1,4,7,4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,
4,1,7,1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,1,4,7,4,1,7,
1,4,7,1,4,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7,4,1,7,4,1,7,1,4,7, ...].
...
生成方法。
从CF=[8]开始,然后重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,36));
z=(1/5)*M[1,1]/M[2,1];CF=控制(z)}
该方法可以如下所示。
z0=[8]=8;
z1=(1/5)*[44]=[8;1,4]=44/5;
z2=(1/5)*[44;37,40]=[8;1,4,7,4,1,7,5]=65204/7405;
z3=(1/5)*[44;37,40,43,40,37,43,41]=[8;1,4,7,4,1,7,1,4、7,1、4、7、1、4,7、4、1、7、4,8]=1467584898352/166668703909;
z4=(1/5)*[44;37,40,43,40,37,43,40,37,43第4、7、1、4、7和4、1、7和1、4和7、4和1、7、4、1和8] = 38573876143771692243421005778572392/4380705980858842541559248009960149 ; ...
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成超过5300位数字*/
{CF=[8];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,36));z=(1/5)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=1200,打印1(楼层(10^(n-1)*z)%10,“,”)
关键词
非n,欺骗
作者
保罗·D·汉纳,2018年10月28日
状态
经核准的
常数z的十进制展开式满足:CF(6*z,n)=CF(z,n。
+10
8
1, 0, 8, 3, 6, 3, 0, 8, 6, 3, 8, 5, 3, 2, 5, 0, 4, 9, 4, 3, 1, 8, 7, 0, 3, 5, 8, 7, 6, 4, 2, 7, 1, 2, 7, 8, 7, 6, 5, 9, 7, 6, 8, 5, 9, 5, 3, 4, 9, 3, 1, 1, 7, 3, 8, 4, 0, 5, 0, 9, 7, 5, 6, 9, 3, 1, 9, 6, 0, 0, 0, 1, 7, 3, 4, 1, 1, 0, 0, 7, 2, 2, 3, 7, 7, 3, 5, 2, 1, 5, 7, 9, 8, 1, 5, 2, 2, 6, 5, 6, 3, 7, 4, 6, 0, 3, 3, 5, 4, 8, 9, 6, 6, 2, 5, 1, 2, 7, 5, 0, 2, 9, 4, 5, 1, 2, 3, 5, 2, 5, 5, 9, 1, 7, 1, 5, 4, 8, 6, 9, 5, 5, 0, 4, 1, 4, 5, 4, 7, 3, 4, 6, 4, 5, 6, 0, 1, 8, 9, 8, 3, 2, 6, 6, 5, 9, 0, 6, 9, 5, 0, 9, 0, 2, 9, 8
抵消
0,3
例子
此常数z的十进制展开式开始于:
z=10.8363086385325049431870358764271278765976859589534931。。。
z的简单连分式展开开始:
z=[10;1,5,9,5,1,9,5,1,9,1,5,9。。。,A321097型(n) ,…];
这样,6*z的简单连分式展开就开始了:
6*z=[65;56、60、64、60、56、64、六十、五十六、64、五十六。。。,A321097型(n) +55,…]。
扩展条款。
z的十进制展开式中的前1000位是
z=10.83630863853250494318703587642712787659768595895349311\
73840509756931960001734110072237735215798152265637\
46033548966251275029451235255917154869550414547346\
45601898326659069509029896766448634581870902999261\
78291099037993947368425232025742840508201019811150\
20208289541868116590985746685817208034834182741861\
61586263073936595659616093596727391439370392218179\
08547782927594504604528661115974783060857978290729\
53554586787471663938331763610007750862560295292956\
22583160832720034539915220107654291931753328805663\
44405451280922502018454665640681719991329902449206\
06333718948414803434770198192597675071144159105469\
40129387536502210902718153383173369508615022733071\
21561771111264471719424048701509094587624798702003\
98051339274318126056502629341701820569809346581703\
17900710636878987844980734936343020769115171474588\
61969660741202379814909712010859009313616125172084\
48790047790048120552938902316397984428482656427316\
35549261064509815824229787948467548551187722067240\
97844304015886508690953002055508602378218606168521...
...
z的连续部分的初始1020项是
z=[10;1,5,9,5,1,9,5A,1,9,1,5,9,15,95,1,5,10,9,10,5,15,9,
5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,
5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,
1,5,9,5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,
5,1,9,1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,1,5,9,5,1,9,
1,5,9,1,5,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9,5,1,9,5,1,9,1,5,9, ...].
...
生成方法。
从CF=[10]开始,然后重复(PARI代码):
{M=contfracpnqn(CF+向量(#CF,i,55));
z=(1/6)*M[1,1]/M[2,1];CF=控制(z)}
这种方法可以说明如下。
z0=[10]=10;
z1=(1/6)*[65]=[10;1,5]=65/6;
z2=(1/6)*[65;56,60]=[10;1,5,9,5,1,9,6]=218525/20166;
z3=(1/6)*[65;56,60,64,60,56,64,61]=[10;1,5,9,5,1,9,1,5,9,1,5,9,1,5,9,5,5,1,9,1,5,10]=30617277049665/28254344201901;
z4=(1/6)*[65;56,60,64,60,56,64,6056,56,56第五、九、一、五、九、五、一、九、一五、九五、五、一九、一十条] = 235326213809918755668077578309692661245/21716455451732827969266335806481498321;
其中,常数z等于上述过程的迭代极限。
黄体脂酮素
(PARI)/*生成超过6000位数字*/
{CF=[10];对于(i=1,8,M=contfracpnqn(CF+向量(#CF,i,55));z=(1/6)*M[1,1]/M[2,1];CF=contfrac(z))}
对于(n=0200,print1(楼层(10^(n-1)*z)%10,“,”)
关键词
非n,欺骗
作者
保罗·D·汉纳2018年10月28日
状态
经核准的

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