世界!O(运行)(f)
N个数字
主页盘子
赢了|

嵌入
回文方形的子集
路德 长度不超过31的所有方形 路德 零星广场 路德
路德 回文平方数 路德 保理化


行程
得分“子集E”=22
得分“子集O”=98
得分“子集U”=21
N个S公司散漫的S公司夸尔P(P)海百合


 普通文本方块      普通文本SSP 

披露的来源


尼尔·斯洛恩“整数序列”可以在线查阅百科全书:
尼尔·斯隆的整数序列
回文方块的子集分类如下:
分离器
%N个n^2是一个零星类型的回文方形。在下面A059744号.
%N个零星类型的回文正方形。在下面A059745号.
分离器
%N个正方形是一个偶数位数的回文。在下面A016113号.
%N个带有偶数位数的回文方块。在下面A027829号.
分离器
%N个Square是一个带有奇数位数的回文。在下面A028816号.
%N个奇数位数的回文方块。在下面A028817号.
分离器
%N个非回文数和“非核心”数的平方表示回文数
位数为奇数。在下面A016106号.
%N个具有奇数位数和非盲的“非核心”的回文正方形
平方根。在下面A028818号.
%N个回文正方形的非对称族。在下面A007573号.
分离器
单击此处查看作者的[P.De Geest先生]表中的条目。
单击此处查看表中关于回文.






偶数长度回文方形
得分“子集O”=98
得分“子集U”=21
N个S公司散漫的S公司夸尔P(P)海百合


索引
编号
办公室。
丁腈橡胶
基数长度
偶数长度的回文平方数长度
   
另请参见斯隆A059744号A059745号
228028 982.503.990.036.767.976.718.486.749.830.91333
965.314.090.438.169.467.661.632.561.053.978.879.350.165.236.166.764.961.834.090.413.56966
218027 633.801.296.960.665.546.843.096.376.103.84833
401.704.084.029.021.754.146.284.676.546.389.983.645.676.482.641.457.120.920.480.407.10466
205268 725.657.034.735.673.961.274.833.643.72530
526.578.132.061.371.126.000.669.458.795.597.854.966.000.621.173.160.231.875.62560
194793 69.697.645.997.692.395.446.140.967.17229
4.857.761.857.619.646.789.399.615.430.880.345.169.939.876.469.167.581.677.58458
182975 64.897.400.105.515.621.177.314.68226
4.211.672.540.455.378.958.718.869.999.688.178.598.735.540.452.761.12452
172673 4.275.548.277.509.699.161.443.65925
18.280.313.073.316.155.472.257.355.375.227.455.161.337.031.308.28150
162176 831.775.153.121.251.039.203.51424
691.849.905.349.880.612.384.525.525.483.216.088.943.509.948.19648
152175 722.956.456.358.957.313.434.53524
522.666.037.791.100.950.480.675.576.084.059.001.197.730.666.22548
141556 3.823.177.109.095.314.778.62122
14.616.683.207.510.408.440.555.504.480.401.570.238.661.64144
131374 637.323.988.797.048.057.09821
406.181.866.696.179.837.389.983.738.971.696.668.181.60442
12741 795.559.265.009.384.10618
632.914.544.142.271.449.944.172.241.445.419.23636
11740 633.856.150.760.638.65218
401.773.619.857.093.475.574.390.758.916.377.10436
10739 404.099.764.753.665.98118
163.296.619.873.968.186.681.869.378.916.692.36136
9640 40.447.213.778.058.76917
1.635.977.102.407.987.117.897.042.017.795.36134
8486 6.819.209.882.215.74216
46.501.623.417.708.833.880.771.432.610.56432
7310 98.275.825.201.58714
9.658.137.819.052.882.509.187.318.56928
6309 69.800.670.077.02814
4.872.133.543.202.112.023.453.312.78428
5264 6.360.832.925.89813
40.460.195.511.188.111.559.106.40426
4162 83.163.115.48611
6.916.103.777.337.773.016.19622
70 64.030.6488
4.099.923.883.299.90416
237 798.6446
637.832.238.73612
115 836
698.8966




ODD长度的零星回文方形
得分“子集E”=22
得分“子集U”=21
N个S公司散漫的S公司夸尔P(P)海百合


索引
编号
办公室。
丁腈橡胶
基数长度
ODD长度的回文平方数长度
   
另请参见斯隆A059744号A059745号
988729 3.109.885.844.380.152.888.763.910.885.950.36334
9.671.389.965.076.056.510.789.702.463.424.611.164.243.642.079.870.156.506.705.699.831.76967
978728 2.602.189.663.685.835.935.193.356.696.699.42434
6.771.391.045.793.403.931.618.552.334.848.680.868.484.332.558.161.393.043.975.401.931.77667
968727 2.199.198.533.628.007.527.429.007.800.357.37234
4.836.474.190.311.578.555.464.055.886.890.474.740.986.885.504.645.558.751.130.914.746.38467
958026 247.310.769.186.488.306.440.493.305.677.95433
61.162.616.555.612.493.985.389.992.772.177.077.127.729.998.358.939.421.655.561.626.11665
948025 228.562.535.427.841.869.726.146.472.478.81533
52.240.832.601.203.469.830.544.252.552.896.269.825.525.244.503.896.430.210.623.804.22565
938022 121.835.770.286.544.029.000.701.461.776.97133
14.843.954.921.315.524.906.513.066.827.400.500.472.866.031.560.942.551.312.945.934.84165
926827 30.698.192.507.926.605.052.067.894.676.19332
942.379.023.253.721.145.582.536.575.330.464.033.575.635.285.541.127.352.320.973.24963
916249 3.144.120.818.001.204.461.096.631.877.16731
9.885.495.718.188.563.066.416.784.240.092.900.424.876.146.603.658.818.175.945.88961
906248 2.633.464.189.244.332.332.100.361.401.58631
6.935.133.636.032.308.614.662.012.098.578.758.902.102.664.168.032.306.363.315.39661
896247 2.522.532.318.987.074601.528.732.897.80631
6.363.169.300.334.308.290.240.718.149.593.959.418.170.420.928.034.330.039.613.63661
886244 1.350.015.677.155.028.833.305.775.848.34131
1.822.542.328.564.351.039.723.668.198.972.798.918.663.279.301.534.658.232.452.28161
876243 1.193.375.854.875.511.918.605.120.376.07931
1.424.145.930.999.858.883.871.649.154.771.774.519.461.783.888.589.990.395.414.24161
866242 1.187.054.882.257.789.974.300.764.887.92931
1.409.099.293.492.055.619.115.210.663.950.593.660.125.119.165.502.943.929.909.04161
855267 228.106.257.936.763.286.220.319.446.69530
52.032.464.909.913.183.706.998.947.070.107.074.989.960.738.131.990.946.423.02559
845265 130.303.161.860.097.498.924.329.036.46930
16.978.913.990.738.767.495.836.054.167.876.145.063.859.476.783.709.931.987.96159
835172 超级棒!    102.956.548.239.095.784.750.974.549.05130
10.600.050.825.309.257.335.789.552.697.979.625.598.753.375.290.352.805.000.60159
824790 13.023.229.862.595.863.669.058.813.03129
169.604.516.054.008.678.101.490.292.111.292.094.101.876.800.450.615.406.96157
814789 11.219.988.402.958.206.841.478.502.21129
125.888.139.762.516.652.901.129.855.030.558.921.109.256.615.267.931.888.52157
803994 2.589.537.706.161.357.166.603.750.27428
6.705.705.531.631.423.370.133.506.726.276.053.310.733.241.361.355.075.07655
793992 1.373.512.530.649.258.635.292.477.60928
1.886.536.671.850.530.641.991.373.196.913.731.991.460.350.581.766.356.88155
783991 1.208.997.217.707.381.836.451.672.37128
1.461.674.272.424.190.432.753.231.165.611.323.572.340.914.242.724.761.64155
773978 1.103.866.360.472.916.946.437.760.98928
1.218.520.941.783.723.816.716.782.817.182.876.176.183.273.871.490.258.12155
763611 307.317.974.379.604.964.632.119.14327
94.445.074.941.362.044.498.184.066.966.048.189.444.026.314.947.054.44953
753610 259.534.999.916.657.357.224.172.37627
67.358.416.181.739.334.421.297.151.315.179.212.443.393.718.161.485.37653
743609 219.293.240.651.172.832.756.867.92227
48.089.525.395.293.201.014.489.455.855.498.441.010.239.259.352.598.08453
733606 122.063.831.551.139.898.460.740.72127
14.899.578.972.945.056.149.893.218.681.239.894.165.054.927.987.599.84153
723605 121.096.650.591.136.334.960.853.87927
14.664.398.784.391.760.063.516.738.283.761.536.006.719.348.789.346.64153
712974 22.859.776.159.292.529.974.209.48526
522.569.366.052.959.132.741.539.313.935.147.231.959.250.663.965.22551
702672 2.198.834.453.254.769.178.871.87225
4.834.872.952.820.199.705.196.890.986.915.079.910.282.592.784.38449
692671 2.107.561.207.005.423.534.632.46225
4.441.814.241.274.157.711.392.425.242.931.177.514.721.424.181.44449
682173 136.569.391.518.194.940.977.04124
18.651.198.699.650.016.285.556.865.558.261.005.699.689.115.68147
671940 25.886.574.803.023.261.617.72623
670.114.755.032.518.816.023.606.320.618.815.230.557.411.07645
661939 25.145.697.104.636.357.696.39423
632.306.082.878.117.302.583.050.385.203.711.878.280.603.23645
651938 20.706.193.716.777.033.766.26823
428.746.458.236.696.712.033.040.330.217.696.632.854.647.82445
641935 12.093.315.807.217.013.334.12123
146.248.287.213.084.882.816.757.618.288.480.312.782.842.64145
631555 3.036.233.455.854.775.865.62322
9.218.713.598.451.835.185.192.915.815.381.548.953.178.12943
621554 2.211.007.906.320.264.673.87822
4.888.555.961.810.720.288.016.108.820.270.181.695.558.88443
611553 2.016.192.509.426.760.663.59822
4.065.032.235.068.578.387.346.437.838.758.605.322.305.60443
601551 1.121.621.184.033.823.231.53922
1.258.034.080.473.435.562.012.102.655.343.740.804.308.52143
591373 263.397.138.410.176.890.08621
69.378.052.522.669.882.013.031.028.896.622.525.087.39641
581372 260.088.804.053.044.407.02621
67.646.185.993.742.928.767.376.782.924.739.958.164.67641
571371 229.359.782.235.085.482.22521
52.605.909.706.925.833.964.246.933.852.960.790.950.62541
561368 128.501.150.236.577.373.66921
16.512.545.612.123.429.216.861.292.432.121.654.521.56141
551082 25.686.162.978.506.292.36620
659.778.968.558.387.244.939.442.783.855.869.877.95639
54950 2.282.211.769.458.230.80519
5.208.490.560.653.668.833.388.663.560.650.948.02537
53947 1.363.859.210.193.543.29119
1.860.111.945.229.755.699.965.579.225.491.110.68137
52738 306.950.094.269.977.05718
94.218.360.372.347.802.120.874.327.306.381.24935
51737 228.138.929.476.341.40518
52.047.371.142.611.077.177.011.624.117.374.02535
50736 207.254.460.945.174.61818
42.954.411.581.674.911.011.947.618.511.445.92435
49734 135.772.344.267.730.05918
18.434.129.467.955.011.411.055.976.492.143.48135
48637 13.661.181.333.262.45917
186.627.875.420.278.656.872.024.578.726.68133
47636 13.593.470.459.544.30917
184.782.439.134.503.767.305.431.934.287.48133
46635 12.797.593.520.483.48117
163.778.399.915.520.777.025.519.993.877.36133
45634 11.863.792.420.598.92917
140.749.570.599.060.595.060.995.075.947.04133
44633 11.843.191.515.764.82117
140.261.185.279.083.838.380.972.581.162.04133
43485 3.138.199.296.186.06716
9.848.294.822.582.726.272.852.284.928.48931
42484 3.107.974.295.870.66316
9.659.504.223.792.743.472.973.224.059.56931
41483 3.066.446.727.654.24316
9.403.095.533.541.415.141.453.355.903.04931
40482 2.564.053.868.197.73416
6.574.372.239.019.762.679.109.322.734.75631
39481 2.201.019.508.986.47816
4.844.486.878.939.076.709.398.786.844.48431
38415 314.155.324.482.86715
98.693.567.900.935.453.900.976.539.68929
37414 210.786.628.549.53815
44.431.002.775.280.908.257.720.013.44429
36411 129.610.990.752.56915
16.799.008.923.862.526.832.980.099.76129
35308 30.395.080.190.57314
923.860.899.791.363.197.998.068.32927
34263 3.069.306.930.69313
9.420.645.034.800.084.305.460.24925
33262 2.634.812.417.86413
6.942.236.477.330.337.746.322.49625
32261 2.149.099.165.35813
4.618.627.222.542.452.227.268.16425
31258 1.349.465.117.84113
1.821.056.104.269.624.016.501.28125
30192 128.817.084.66912
16.593.841.302.620.314.839.56123
29191 112.247.658.96112
12.599.536.942.224.963.599.52123
28190 111.283.619.36112
12.384.043.938.083.934.048.32123
27178 101.116.809.85112
10.224.609.234.443.290.642.20123
26161 30.693.069.30711
942.064.503.484.305.460.24921
25160 30.101.273.64711
906.086.675.171.576.680.60921
24159 22.865.150.135美元11
522.815.090.696.090.518.22521
23156 13.579.355.05911
184.398.883.818.388.893.48121
22137 10.207.355.54911
104.190.107.303.701.091.40121
21130 2009年6月10日11
102.132.537.636.735.231.20121
20113 2.481.623.25410
6.158.453.974.793.548.51619
19112 2.062.386.21810
4.253.436.912.196.343.52419
1895 306.930.6939
94.206.450.305.460.24917
1769 30.001.2538
900.075.181.570.00915
1667 12.866.6698
165.551.171.155.56115
1566 12.028.2298
144.678.292.876.44115
1465 11.129.3618
123.862.676.268.32115
1356 3.069.3077
9.420.645.460.24913
1255 2.294.6757
5.265.533.355.62513
1154 2.012.7487
4.051.154.511.50413
1051 1.270.8697
1.615.108.015.16113
944 1.042.1517
1.086.078.706.80113
831 30.6935
942.060.2499
730 24.8465
617.323.7169
629 22.8655
522.808.2259
520 2.6364
6.948.4967
419 2.2854
5.221.2257
14 307
94.2495
213 264
69.6965
17 262
676




超方形回文
得分“子集E”=22
得分“子集O”=98
N个S公司散漫的S公司夸尔P(P)海百合
大卫·格里菲斯威斯康星大学麦迪逊分校名誉教授
退休后玩方形回文。他发现了一个可爱的特例,想知道
您知道以前关于数字的讨论中有这三个附加属性:

(i) 所有数字均为正数;
(ii)数字之和是一个完美的平方;
(iii)数字的乘积是一个完美的正方形。

他发现了21个例子:
16带有二进制(所有数字0或1)平方根,无需计算机搜索即可识别,
1来自Even Root系列(最小的USP),
1包含数字0、1或9的非对称基数,以及
搜索表中的零星条目。

大卫还推测这些都是具有额外属性(i)-(iii)的示例。
此外,他推测只有有限多个所有数字都为正的方形回文。


索引
编号
办公室。
丁腈橡胶
基数长度
超方形回文长度
   
大卫·格里菲斯
他们推测只有21个USP(参见PDF文章)
21741 795.559.265.009.384.10618
632.914.544.142.271.449.944.172.241.445.419.23636
20628 11.100.100.100.11117
123.212.222.232.242.494.242.232.222.212.32133
19410 111.100.010.001.11115
12.343.212.222.246.964.222.221.234.32129
18408 111.010.010.010.11115
12.323.222.322.444.944.422.322.232.32129
17406 111.001.010.100.11115
12.321.224.243.244.944.234.242.212.32129
16397 110.101.010.101.01115
12.122.232.425.262.926.252.423.222.12129
15257 1.111.001.001.11113
1.234.323.224.469.644.223.234.32125
14255 1.110.101.010.11113
1.232.324.252.649.462.524.232.32125
13253 1.110.011.100.11113
1.232.124.642.369.632.464.212.32125
12248 1.101.101.011.01113
1.212.423.436.449.446.343.242.12125
11246 1.101.011.101.01113
1.212.225.444.549.454.445.222.12125
10156 13.579.355.05911
184.398.883.818.388.893.48121
9155 11.110.101.11111
123.434.346.696.643.434.32121
8153 11.101.110.11111
123.234.645.696.546.432.32121
7148 11.011.111.01111
121.244.565.696.565.442.12121
6113 2.481.623.25410
6.158.453.974.793.548.51619
592 111.111.1119
12.345.678.987.654.32117
490 111.091.1119
12.341.234.943.214.32117
24 11.0115
1.212.42.12110
217 1.1114
1.234.3217
112 212
44.9445






N个S公司散漫的S公司夸尔P(P)海百合Pari/gp脚本生成器
得分“子集E”=22
得分“子集O”=98
得分“子集U”=21


我非常感激大卫·格里菲斯,我的回文方块教练,他鼓励我编程
我引用“由于四个无限族中的每个族的设计都非常简单
最好使用一个程序来枚举那些远远超过任何完整列表的任何所需大小
零星的可能。即使是不对称的家庭也应该能很好地应对案件
检查回文属性。

那么,请允许我向您展示我最后一个编写的NSSP(非零星方形回文)完整列表生成器
在Pari/gp代码中。该程序处理所有非零星类别。复制/粘贴代码
在下面您最喜欢的文本编辑器中,另存为“nssp.gp”。把它们列在更长的列表中可以减轻我的负担
无聊的桌子。这四个类别包括

1.EVEN根系列
2.BINARY根系列
3.TERNARY根家族
4.不对称系列

您将在文件“nssp.txt”中以非常有序的方式找到每个基数长度的所有条目。
你可以用任何合适的文本编辑器来阅读这个文件。在屏幕上,你会看到一个无序列表在滚动。
一些注意事项
使用文本编辑器更改变量的值bnl公司(basenumber length(⩾2),设置为31),可以根据需要调整。
请确保文件夹“C:/pari/”的路径存在,否则会发生错误。当然可以随意更改其名称。


Pscr()=++;print(of,“”,b,“{BL=”,bnl,“}”,bq,“{PL=”,#数字(bq),“}”);{bnl=31;=0;pr=(bnl/2!=bnl/2);如果(pr,b=2*10^(bnl-1)+10^;silo=列表(b);bq=b^2;Pscr(),思洛存储器=列表();bg=3^(bnl\2-1+pr);对于(i=bg,bg*2,li=数字(i,3);b=来自数字(concat(li,Vecrev(li[1..#(li)-pr]));bq=b^2;如果(数字(bq)==Vecrev(数字(b q)),Pscr();listput(思洛存储器,b));bg=2^(bnl\2-1+pr);对于(i=bg,bg*2,li=二进制(i);b=来自数字(concat(li,Vecrev(li[1..#(li)-pr]));对于(y=0,bnl\4,b=数字(b);b[bnl\2+1-y]=9;b[bnl\2-y]=0;b=来自数字(b);bq=b^2;如果(数字(bq)==Vecrev(数字(b q)),i++;Pscr();listput(思洛存储器,b));列表排序(思洛存储器);=0;ps=“c: /pari/nssp.txt“;写入1(ps,”\n“);对于(s=1,#(筒仓),b=筒仓[s];bq=b^2;++的;write(ps,of,“(PG4)”,b,“{BL=”,bnl,“}[”,bq,“]{PL=”,#数字(bq),“}”);}


以下是“nssp.txt”的输出示例bnl=9.
注意以黄色突出显示的两个不对称解,以蓝色突出显示的具有三元根的四个解和
Even Root家族的最后两个绿色!其余白色部分来自二进制根系列。


1(第4页)100000001{BL=9}【10000000200000001】{PL=17}2(PG4)100010001{BL=9}[10002000300020001]{PL=17}3(第4组)100020001{BL=9}[10004000600040001]{PL=17}4(PG4)100101001{BL=9}[100202010401202001]{PL=17}5(PG4)100111001{BL=9}[10022212521222001]{PL=17}6(PG4)100121001{BL=9}[10024214841242001]{PL=17}7(PG4)101000101{BL=9}[10201020402010201]{PL=17}8(PG4)101010101{BL=9}[1020340504030201]{PL=17}9(PG4)101020101{BL=9}[10205060806050201]{PL=17}10(PG4)101101101{BL=9}[10221432623412201]{PL=17}11(PG4)101111101{BL=9}[10223454745432201]{PL=17}12(PG4)110000011{BL=9}[1210002420000121]{PL=17}13(PG4)11001011{BL=9}[1210220520220121]{PL=17}14(PG4)110020011{BL=9}[1210440282044012]{PL=17}15(PG4)110091011{BL=9}[121220030703002121]{PL=17}16(PG4)110101011{BL=9}[121222232622121]{PL=17}17(PG4)110111011{BL=9}[12124434743442121]{PL=17}18(PG4)111000111{BL=9}[1232102464212321]{PL=17}19(PG4)111010111{BL=9}[123232447442321]{PL=17}20(PG4)111091111{BL=9}[1234123494321]{PL=17}21(第4页)111101111{BL=9}[122344566865434321]{PL=17}22(PG4)111111111{BL=9}[12345678987654321]{PL=17}23(PG4)200000002{BL=9}[4000000800000004]{PL=17}24(PG4)200010002{BL=9}[40004000900040004]{PL=17}


以下较短的Pari程序为B、T、A、E四个系列中的每一个生成单独的屏幕输出。
将bnl的蓝色值替换为所选基数的数字长度。

首先是二进制家族[B]

{bnl=33;=0;pr=(bnl/2!=bnl\2);bg=2^(bnl\2-1+pr);对于(i=bg,bg*2-1,li=二进制(i);b=来自数字(concat(li,Vecrev(li[1..#(li)-pr]));bq=b^2;如果(数字(bq)==Vecrev(数字(b q)),则为++;打印(共,“”,b,“{BL=”,bnl,“}”,bq,“{PL=”,#位(bq),“}”);}


接下来是三元系[T]

Pscr()=++;b=来自数字(b);打印(第页,共页,“”,b,“{BL=”,bnl,“}”,b^2,“{PL=”,#位(b^2),”}“);{bnl=33;如果((-1)^bnl==-1,b=数字(10^(bnl-1)+2*10^(bnl\2)+1);=0;Pscr();a=1;对于(i=bnl\2+2,bnl-1,b=数字(b);b[i]=1;b[i-2*a]=1;Pscr();b=数字(b);b[i]=0;b[i-2*a]=0;a+=1;b=从数字(b)开始),打印(“如果bnl(=“,bnl,”)为偶数,则无解决方案”);}


在此之后,请允许我介绍不对称家族[A]

{bnl=33;=0;pr=(bnl/2!=bnl\2);bg=2^(bnl\2-1+pr);对于(i=bg,bg*2-1,li=二进制(i);b=来自数字(concat(li,Vecrev(li[1..#(li)-pr]));对于(y=0,bnl\4,b=数字(b);b[bnl\2+1-y]=9;b[bnl\2-y]=0;b=来自数字(b);bq=b^2;如果(数字(bq)==Vecrev(数字(b q)),则为++;i++;打印(第页,共页,“”,b,“{BL=”,bnl,“}”,bq,“{PL=”,#位(bq),”}“));}


最后是偶根家族[E]

Pscr()=++;b=来自数字(b);打印(第页,共页,“”,b,“{BL=”,bnl,“}”,b^2,“{PL=”,#位(b^2),”}“);{bnl=33;b=数字(2*10^(bnl-1)+2);=0;Pscr();如果((bnl/2!=bnl\2),b=数字(b);b[bnl\2+1]=1;Pscr());}












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(©保留所有权利)-上次修改日期:2023年12月22日。
Patrick De Geest-比利时旗帜-简短的个人简历-一些图片
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