倒过来写的平方数

northwolves

(1), 第2025个数是几？
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1. a=Union@Table[FromDigits@Reverse[IntegerDigits[k^2]],{k,10000}];a[[2025]]

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6148035

第2304个平方数的逆转

王守恩

northwolves 发表于 2025-2-13 08:09
(2), 5202是第几个数？
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这个很简单啊，1-45逆转，去掉10的倍数，第41个 ...

5202是第56个数？
Table[a = Union@Table[IntegerReverse[k^2], {k, 1000}]; a[[n]], {n, 56}]
{1, 4, 9,
18, 46, 52, 61, 63, 94,
121, 144, 148, 163, 169, 423, 441, 484, 487, 522, 526, 652, 675, 676, 691, 925, 927, 961, 982,
1042, 1062, 1089, 1251, 1273, 1297, 1405, 1426, 1656, 1674, 1828, 1843, 1861, 4032, 4069, 4072, 4201, 4264, 4276, 4441, 4477, 4483, 4633, 4648, 4671, 4806, 4815, 5202}

Union[Table[IntegerReverse[k^2], {k, 90}]]——这个无法排序(困扰我好久)。谢谢！！！

northwolves

1. FirstPosition[Union@IntegerReverse[Range@100^2], 5202]

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王守恩

northwolves 发表于 2025-2-13 13:44

这些数没有规律。譬如：前后两数的差。

{427, 1173, 93, 44, 157, 581, 1143, 34, 57, 3, 203, 529, 12309, 483, 234, 53, 43, 1056, 66, 50, 4, 222, 431, 1288, 120, 14, 103, 176, 1683, 103, 122, 61, 282, 1551, 104, 223, 9, 218, 67, 10236, 137, 67, 108, 5, 142, 1431, 479, 238}

1. Table[a = Union@Table[IntegerReverse[k^2], {k, 1000}]; a[[n + 1]], {n, 300, 347}] - Table[a = Union@Table[IntegerReverse[k^2], {k, 1000}]; a[[n]], {n, 300, 347}]

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再譬如。
1位数最大=3。
2位数最大=7。
3位数最大=17。
3位数最大=83。
5位数最大=167。
6位数最大=583。
7位数最大=1833。
8位数最大

王守恩

1. Table[a = Union@Table[IntegerReverse[k^2], {k, 1000}]; a[[n]], {n, 300, 387}]

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{104409, 104836, 106009, 106102, 106146, 106303, 106884, 108027, 108061, 108118, 108121, 108324, 108853, 121162, 121645, 121879, 121932, 121975, 123031, 123097, 123147, 123151,
123373, 123804, 125092, 125212, 125226, 125329, 125505, 127188, 127291, 127413, 127474, 127756, 129307, 129411, 129634, 129643, 129861, 129928, 140164, 140301, 140368, 140476,
140481, 140623, 142054, 142533, 142771, 142786, 142801, 142848, 144135, 144172, 144495, 144859, 144922, 146277, 146341, 146583, 146593, 146731, 146857, 148122, 148249, 148606,
148915, 148972, 161383, 161541, 161557, 161631, 161677, 161893, 163132, 163195, 163269, 163435, 163962, 165096, 165448, 165571, 165733, 165744, 165901, 167076, 167101, 167323}

这些数没有规律。譬如：前后两数的差。
a(301)-a(300) = 104836 - 104409 = 427,   
a(302)-a(301) = 106009 - 104836 = 1173,
a(303)-a(302) = 106102 - 106009 = 93,
a(304)-a(303) = 106146 - 106102 = 44,
a(305)-a(304) = 106303 - 106146 = 157,

{427, 1173, 93, 44, 157, 581, 1143, 34, 57, 3, 203, 529, 12309, 483, 234, 53, 43, 1056, 66, 50, 4, 222, 431, 1288, 120, 14, 103, 176, 1683, 103, 122, 61, 282, 1551, 104, 223, 9, 218, 67, 10236, 137, 67, 108, 5, 142, 1431, 479, 238}

1. Table[a = Union@Table[IntegerReverse[k^2], {k, 1000}]; a[[n + 1]], {n, 300, 347}] - Table[a = Union@Table[IntegerReverse[k^2], {k, 1000}]; a[[n]], {n, 300, 347}]

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王守恩

再譬如。
1位数最小=1。
2位数最小=9。
3位数最小=11。
3位数最小=49。
5位数最小=249。
6位数最小=601。
7位数最小=1249。
8位数最小=5001。

5楼这串数——3, 6, 19, 62, 195, 615, 1946, 6154, 19460, 61540, 194605, 615395, 1946050, 6153950, 19460499, 61539501, 194604990, 615395010, 1946049894, 也有问题。

王守恩

要不丢了？不可惜！不浪费你宝贵的时间。另外一个题目。

A056792——从 0 到 2024,  只能 + 1, × 2,  最快几步？想个办法——把2024直接拉出来。谢谢！

A056792——只会从1开始——1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7}

f[n_] := Floor@Log2@n + DigitCount[n, 2, 1]; Array[f, 64]

再一个题目——从 0 到 2024,  只能 + 1, × 3,  最快几步？想个办法——把2024直接拉出来。我还是玩不出来。谢谢！

northwolves

王守恩 发表于 2025-2-14 06:38
要不丢了？不可惜！不浪费你宝贵的时间。另外一个题目。

A056792——从 0 到 2024,  只能 + 1, × 2,  最 ...

1. f[n_] := IntegerLength[n, 3] - 1 +
   
2.   Total@IntegerDigits[n, 3];
   
3. Array[f, 100]
   
4. f[2024]

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{1,2,2,3,4,3,4,5,3,4,5,4,5,6,5,6,7,4,5,6,5,6,7,6,7,8,4,5,6,5,6,7,6,7,8,5,6,7,6,7,8,7,8,9,6,7,8,7,8,9,8,9,10,5,6,7,6,7,8,7,8,9,6,7,8,7,8,9,8,9,10,7,8,9,8,9,10,9,10,11,5,6,7,6,7,8,7,8,9,6,7,8,7,8,9,8,9,10,7,8}
18

northwolves

1. f[x_, k_] := Nest["(" <> ToString@# <> "+1)" &, x, k] <> "*3"
   
2. g[n_] := StringTake[Fold[f, 0, Reverse@IntegerDigits[n, 3]], {1, -3}];
   
3. g[2024]
   

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"((((((((((((0+1)+1)*3+1)+1)*3+1)+1)*3+1)+1)*3*3+1)+1)*3+1)+1)"

王守恩

northwolves 发表于 2025-2-15 10:35
{1,2,2,3,4,3,4,5,3,4,5,4,5,6,5,6,7,4,5,6,5,6,7,6,7,8,4,5,6,5,6,7,6,7,8,5,6,7,6,7,8,7,8,9,6,7,8,7 ...

Table[d[n_] := IntegerLength[n, k] - 1 + Total[IntegerDigits[n, k]]; Array[d, 50], {k, 2, 9}]
{1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 06, 6, 7, 6, 7, 7, 08, 6, 07, 07, 08, 7, 08, 08, 09, 6, 07, 07, 08, 7, 08, 08, 09, 07, 08, 08, 09, 08, 09, 09, 10, 07, 08, 08, 09, 08, 09, 09, 10, 8, 09, 09, 10, 09, 10, 10, 11, 07, 08, 08, 09, 08, 09, 09},
{1, 2, 2, 3, 4, 3, 4, 5, 3, 4, 5, 4, 5, 6, 5, 6, 07, 4, 5, 6, 5, 6, 07, 6, 07, 08, 04, 5, 06, 05, 06, 7, 06, 07, 08, 5, 06, 07, 06, 07, 08, 07, 08, 09, 06, 07, 08, 07, 08, 09, 08, 09, 10, 05, 06, 7, 06, 07, 08, 07, 08, 09, 06, 07, 08, 07, 08, 09, 08, 09},
{1, 2, 3, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 3, 04, 5, 6, 4, 5, 6, 07, 5, 06, 07, 08, 6, 07, 08, 09, 4, 05, 06, 07, 5, 06, 07, 08, 06, 07, 08, 09, 07, 08, 09, 10, 05, 06, 07, 08, 06, 07, 08, 09, 7, 08, 09, 10, 08, 09, 10, 11, 04, 05, 06, 07, 05, 06, 07},
{1, 2, 3, 4, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 06, 7, 8, 5, 6, 7, 08, 9, 03, 04, 05, 6, 07, 04, 05, 6, 07, 08, 05, 6, 07, 08, 09, 06, 07, 08, 09, 10, 07, 08, 09, 10, 11, 04, 05, 06, 07, 08, 05, 6, 07, 08, 09, 06, 07, 08, 09, 10, 07, 08, 09, 10, 11, 08},
{1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 08, 4, 5, 6, 7, 8, 09, 5, 06, 07, 08, 9, 10, 06, 07, 8, 09, 10, 11, 3, 04, 05, 06, 07, 08, 04, 05, 06, 07, 08, 09, 05, 06, 07, 08, 09, 10, 06, 07, 8, 09, 10, 11, 07, 08, 09, 10, 11, 12, 08, 09, 10, 11, 12},
{1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 06, 7, 8, 9, 4, 5, 06, 7, 08, 09, 10, 5, 06, 07, 08, 9, 10, 11, 06, 7, 08, 09, 10, 11, 12, 07, 08, 09, 10, 11, 12, 13, 03, 04, 05, 06, 07, 08, 09, 4, 05, 06, 07, 08, 09, 10, 05, 06, 07, 08, 09, 10, 11, 06},
{1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 9, 3, 04, 5, 6, 7, 8, 9, 10, 4, 05, 06, 07, 8, 09, 10, 11, 5, 06, 07, 08, 9, 10, 11, 12, 06, 07, 08, 09, 10, 11, 12, 13, 07, 08, 09, 10, 11, 12, 13, 14, 8, 09, 10, 11, 12, 13, 14, 15, 03, 04, 05, 06, 07, 08, 09},
{1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 08, 9, 10, 11, 04, 5, 06, 07, 08, 9, 10, 11, 12, 5, 06, 07, 08, 09, 10, 11, 12, 13, 06, 07, 08, 09, 10, 11, 12, 13, 14, 07, 08, 9, 10, 11, 12, 13, 14, 15, 08, 09, 10, 11, 12, 13, 14, 15}}