斐波那契数
目录
递归方程
正在生成函数
-
k个 = 1: 10 / 89 = 0.11235955056179775280898876404...
-
k个 = 2: 100 / 9899 = 0.010102030508132134559046368320...
-
k个 = 3: 1000 / 998999 = 0.0010010020030050080130210340550...
-
k个 = 4: 10000 / 99989999 = 0.00010001000200030005000800130021...
-
k个 = 1: 1 / 89 = 0.011235955056179775280898876404... ( A021093号 )
-
k个 = 2: 1 / 9899 = 0.00010102030508132134559046368320...
-
k个 = 3: 1 / 998999 = 0.0000010010020030050080130210340550...
-
k个 = 4: 1 / 99989999 = 0.000000010001000200030005000800130021...
比奈封闭式公式
斐波那契函数
连续商的极限
公式
偶数指数斐波那契数
-
{0, 1, 3, 8, 21, 55, 144, 377, 987, 2584, 6765, 17711, 46368, 121393, 317811, 832040, 2178309, 5702887, 14930352, 39088169, 102334155, 267914296, 701408733, 1836311903, ...}
奇指数斐波那契数
-
{1, 1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437, 1134903170, 2971215073, ...}
斐波那契数mod n个
-
{0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 5, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 5, 8, 10, 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 0, 1, 2, 3, ...}
-
{1、2、3、4、5、6、7、6、9、10、7、11、9、14、15、11、13、12、20、9、14、19、13、25、18、27、21、10、30、19、21、19、13、35、15、29、13、25、30、19、18、33、20、45、21、15、15、37、50、35、30、37、29、12、25、…}
-
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 1, 4, 0, 0, 5, 4, 7, 7, 0, 12, 8, 4, 11, 0, 8, 0, 7, 19, 0, 12, 11, 14, 21, 0, 21, 8, 25, 14, 10, 22, 24, 10, 24, 0, 25, 32, 33, 12, 0, 16, 22, 16, 25, 43, 31, 24, 38, 22, 5, 36, 41, ...}
-
{1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 15, 20, 25, 27, 30, 35, 45, 50, 70, 75, 81, 100, 125, 135, 150, 175, 225, 243, 250, 350, 375, 405, 500, 625, 675, 729, 750, 875, 1125, 1215, 1250, 1750, 1875, 2025, 2187, ...}
-
{1, 2, 3, 4, 5, 8, 11, 21, 29, 55, 76, 144, 199, 377, 521, 987, 1364, 2584, 3571, 6765, 9349, 17711, 24476, 46368, 64079, 121393, 167761, 317811, 439204, 832040, 1149851, 2178309, 3010349, 5702887, ...}
-
{0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 0, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 0, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 0, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 0, 1, 1, 2, 3, 5, ...}
-
{0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1, 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, ...}
-
{0,1,1,2,3,5,8,1,9,10,7,5,0,5,5,10,3,1,4,5,2,11,1,0,1,1,2,3,5,8,1,9,10,7,5,0,5,5,10,3,1,4,5,9,2,11,1,0,1,2,3,5,8,1,9,10,7,5,0,5,10,3,1,4,5,9,2,11,1,0,…}
-
{0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, 1, 0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, 1, 0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, ...}
-
{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 44, 33, 77, 10, 87, 97, 84, 81, 65, 46, 11, 57, 68, 25, 93, 18, 11, 29, 40, 69, 9, 78, 87, 65, 52, 17, 69, 86, 55, 41, 96, 37, 33, 70, 3, 73, 76, 49, 25, 74, 99, 73, 72, 45, ...}
皮萨诺时期
-
{1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, ...}
-
{1, 2, 4, 5, 10, 10, 13, 11, 17, 22, 9, 23, 19, 37, 20, 23, 25, 19, 17, 53, 15, 25, 37, 23, 50, 61, 53, 45, 13, 58, 29, 47, 39, 25, 77, 23, 55, 17, 47, 59, 31, 37, 65, 29, 93, 37, 25, 23, 81, 148, 67, 75, 77, 53, 19, ...}
Pisano周期最小的数字
-
{8, 11, 21, 29, 55, 76, 144, 199, 377, 521, 987, 1364, 2584, 3571, 6765, 9349, 17711, 24476, 46368, 64079, 121393, 167761, 317811, 439204, 832040, 1149851, 2178309, 3010349, 5702887, 7881196, ...}
斐波那契素数
-
{2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, ...}
-
{3、4、5、7、11、13、17、23、29、43、…}
序列
-
{1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 21, 24, 25, 26, 27, 30, 32, 34, 36, 39, 40, 42, 45, 48, 50, 52, 54, 55, 60, 63, 64, 65, 68, 72, 75, 78, 80, 81, 84, 89, 90, 96, ...}
??? {1, 2, 3, 4, 5, 7, 8, 11, 13, 17, 21, 34, 55, ...} ??? (可能缺少从1到55的某些术语…)
-
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, ...}
另请参见
-
{{ 斐波那契 }} (数学函数模板)