A029795 -id:A029795 - cp's OEIS frontend

A029793 Numbers k such that k and k^2 have the same set of digits.

0, 1, 10, 100, 1000, 4762, 4832, 10000, 10376, 10493, 11205, 12385, 12650, 14829, 22450, 23506, 24605, 26394, 34196, 36215, 47620, 48302, 48320, 49827, 64510, 68474, 71205, 72510, 72576, 74510, 74528, 79286, 79603, 79836, 94583, 94867, 96123, 98376

Offset: 1

Patrick De Geest

This sequence has density 1: almost all numbers k have all 10 digits in both k and k^2. - Franklin T. Adams-Watters, Jun 28 2011

			{0, 1, 3, 4, 9} = digits of a(10) = 10493 and of 10493^2 = 110103049;
{0, 1, 2, 5, 6} = digits of a(100) = 162025 and of 162025^2 = 26252100625;
{0, 1, 3, 4, 6, 7, 8} = digits of a(1000) = 1764380 and of 1764380^2 = 3113036784400;
{1, 2, 3, 4, 7, 8, 9} = digits of a(10000) = 14872239 and of 14872239^2 = 221183492873121.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A029795, A029797, A030091; A178501 is a subsequence, A054038, A171102, A232659-A232662.

import Data.List (nub, sort)
a029793 n = a029793_list !! (n-1)
a029793_list = filter (\x -> digs x == digs (x^2)) [0..]
   where digs = sort . nub . show
-- Reinhard Zumkeller, Jun 27 2011

[ n: n in [0..10^5] | Set(Intseq(n)) eq Set(Intseq(n^2)) ];  // Bruno Berselli, Jun 28 2011

seq(`if`(convert(convert(n,base,10),set) = convert(convert(n^2,base,10),set), n, NULL), n=0..100000); # Nathaniel Johnston, Jun 28 2011

digitSet[n_] := Union[IntegerDigits[n]]; Select[Range[0, 99000], digitSet[#] == digitSet[#^2] &] (* Jayanta Basu, Jun 02 2013 *)

isA029793(n)=Set(Vec(Str(n)))==Set(Vec(Str(n^2))) \\ Charles R Greathouse IV, Jun 28 2011

(0L to 99999L).filter(n => n.toString.toCharArray.toSet == (n * n).toString.toCharArray.toSet) // Alonso del Arte, Jan 19 2020

A232659 Numbers n such that n and n^4 have the same set of digits.

Original entry on oeis.org

0, 1, 10, 100, 1000, 10000, 35641, 100000, 129486, 146980, 356410, 465780, 1000000, 1059281, 1083749, 1206794, 1239876, 1245890, 1265360, 1294860, 1297853, 1348970, 1469800, 1486920, 1495860, 1567038, 1572086, 1574689, 1956740, 2035817, 2084615, 2114760

Offset: 1

Arkadiusz Wesolowski, Nov 27 2013

			{1, 3, 4, 5, 6} - the set of digits of 35641 and of 35641^4, so 35641 is in the sequence.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A029793, A029795, A232660-A232662.

[n : n in [0..2114760] | Set(Intseq(n)) eq Set(Intseq(n^4))];

Select[Range[0,22*10^5],Union[IntegerDigits[#]]== Union[ IntegerDigits[ #^4]]&] (* Harvey P. Dale, Aug 02 2016 *)

for(n=0, 2114760, if(Set(Vec(Str(n)))==Set(Vec(Str(n^4))), print1(n, ", ")));

A232662 Numbers n such that n and n^7 have the same set of digits.

Original entry on oeis.org

0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 12635940, 26875130, 29851046, 31572460, 36082794, 38625410, 39756810, 42675139, 47025831, 50748936, 58291760, 65279801, 68249735, 76942451, 78952160, 80572614, 100000000, 102359784, 102374865

Offset: 1

Arkadiusz Wesolowski, Nov 27 2013

			{0, 1, 2, 3, 4, 5, 6, 9} - the set of digits of 12635940 and of 12635940^7, so 12635940 is in the sequence.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A029793, A029795, A232659-A232661.

for(n=0, 102374865, if(Set(Vec(Str(n)))==Set(Vec(Str(n^7))), print1(n, ", ")));

A029797 Numbers k such that k^2 and k^3 have the same set of digits.

Original entry on oeis.org

0, 1, 10, 100, 146, 1000, 1203, 1460, 7652, 8077, 8751, 8965, 10000, 10406, 11914, 12030, 12057, 12586, 12768, 12961, 13055, 14202, 14600, 14625, 16221, 19350, 20450, 21539, 22040, 22175, 23682, 24071, 25089, 25201, 25708, 26653, 26981

Offset: 1

Patrick De Geest

Conjecture: there exists some m and N for which a(n) = m + n for all n >= N. [Charles R Greathouse IV, Jun 28 2011]

This conjecture is false. If the conjecture is true then for some N we would have k is in the sequence if k >= n. But 10^e + 1 (A062397) is not in the sequence for any integer e >= 0. - David A. Corneth, Nov 13 2023

			146 is in the sequence as 146^2 = 21316 has digits {1, 2, 3, 6} and 146^3 = 3112136 has digits {1, 2, 3, 6} as well. - _David A. Corneth_, Nov 13 2023

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A029793, A029795, A029800, A062397.

Cf. A011557 (a subsequence).

[ n: n in [0..34*10^4] | Set(Intseq(n^2)) eq Set(Intseq(n^3)) ];  // Bruno Berselli, Jun 28 2011

isA029797(n)=Set(Vec(Str(n^2)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011

A232660 Numbers n such that n and n^5 have the same set of digits.

Original entry on oeis.org

0, 1, 10, 100, 1000, 10000, 39568, 100000, 395680, 1000000, 2114325, 2751490, 3246105, 3956800, 4356891, 4768209, 4926051, 6274019, 8021439, 10000000, 10267394, 10352849, 10368279, 10456932, 10478632, 10489723, 10489725, 10527934, 10567293, 10639428, 10827439

Offset: 1

Arkadiusz Wesolowski, Nov 27 2013

			{3, 5, 6, 8, 9} - the set of digits of 39568 and of 39568^5, so 39568 is in the sequence.

Lars Blomberg, Table of n, a(n) for n = 1..10000
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014

Cf. A029793, A029795, A232659, A232661, A232662.

[n : n in [0..10827439] | Set(Intseq(n)) eq Set(Intseq(n^5))];

for(n=0, 10827439, if(Set(Vec(Str(n)))==Set(Vec(Str(n^5))), print1(n, ", ")));

A232661 Numbers n such that n and n^6 have the same set of digits.

Original entry on oeis.org

0, 1, 10, 100, 1000, 10000, 100000, 1000000, 1380796, 10000000, 10423786, 10489362, 10532689, 10689247, 10743958, 12645980, 13042697, 13674925, 13807960, 14205893, 14857690, 16892043, 17284360, 17983256, 19046537, 19754203, 20634971, 20637451, 21865409

Offset: 1

Arkadiusz Wesolowski, Nov 27 2013

			{0, 1, 3, 6, 7, 8, 9} - the set of digits of 1380796 and of 1380796^6, so 1380796 is in the sequence.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A029793, A029795, A232659, A232660, A232662.

for(n=0, 21865409, if(Set(Vec(Str(n)))==Set(Vec(Str(n^6))), print1(n, ", ")));

A232712 Least positive k (not a power of 10) such that k and k^n have the same set of digits.

Original entry on oeis.org

2, 4762, 107624, 35641, 39568, 1380796, 12635940, 40837596, 102349857, 102567384, 106342987, 129046873, 107623945, 231940678, 239607415, 368709154, 1023456789, 164758903, 176384592, 1023456789, 1023456789, 1023456789, 1023456789, 1023456789, 1023456789

Offset: 1

Arkadiusz Wesolowski, Nov 28 2013

a(17) and a(20)-a(40) = A050278(1) = 1023456789, the smallest pandigital number. [Lars Blomberg, Dec 10 2013]

Lars Blomberg, Table of n, a(n) for n = 1..40

Cf. A171102, A029793, A029795, A232659-A232662.

for(n=1, 6, k=1; until(Set(Vec(Str(k)))==Set(Vec(Str(k^n)))&&!(sumdigits(k)==1), k++); print1(k, ", "));

a(14)-a(25) from Lars Blomberg, Dec 10 2013

A029796 Cubes k such that cube root of k and k have the same set of digits.

Original entry on oeis.org

0, 1, 1000, 1000000, 1000000000, 1000000000000, 1000000000000000, 1246600760666624, 1315559990715517, 2325413183184125, 2663883812634624, 4050549951695416, 4544600014144000

Offset: 1

Patrick De Geest

Cf. A029795.

a(n) = A029795(n)^3. - Andrew Howroyd, Aug 11 2024

Offset corrected by Andrew Howroyd, Aug 11 2024

A030092 Primes p such that p and p^3 have the same set of digits.

Original entry on oeis.org

1035743, 1045573, 1215397, 1396247, 1642309, 2031487, 2149573, 2363149, 2458019, 2569751, 2815973, 2857319, 2986301, 3349517, 3482461, 3530467, 3865079, 4332871, 4387291, 4631489, 4893617, 5170283, 5749013, 5784319

Offset: 1

Patrick De Geest

Intersection of A029795 and A000040.

Select[Prime[Range[400000]],Union[IntegerDigits[#]] == Union[ IntegerDigits[ #^3]]&] (* Harvey P. Dale, Aug 26 2013 *)

Offset changed by Andrew Howroyd, Aug 11 2024

cp's OEIS Frontend

A029793 Numbers k such that k and k^2 have the same set of digits.

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A232659 Numbers n such that n and n^4 have the same set of digits.

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A232662 Numbers n such that n and n^7 have the same set of digits.

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A029797 Numbers k such that k^2 and k^3 have the same set of digits.

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A232660 Numbers n such that n and n^5 have the same set of digits.

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A232661 Numbers n such that n and n^6 have the same set of digits.

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A232712 Least positive k (not a power of 10) such that k and k^n have the same set of digits.

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A029796 Cubes k such that cube root of k and k have the same set of digits.

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