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

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

1,3

Comments

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

Links

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

Example

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

Prog

(Magma) [ n: n in [0..34*10^4] | Set(Intseq(n^2)) eq Set(Intseq(n^3)) ];  // Bruno Berselli, Jun 28 2011
(PARI) isA029797(n)=Set(Vec(Str(n^2)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011

Crossrefs

Cf. A029793, A029795, A029800, A062397.

Cf. A011557 (a subsequence).

Sequence in context: A207585 A208381 A031187 * A367593 A206983 A207841

Adjacent sequences: A029794 A029795 A029796 * A029798 A029799 A029800

Keyword

nonn,base

Author

Patrick De Geest

Status

approved