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

Author

Patrick De Geest

Keywords

• nonn
• base

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

Examples

			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
		

Links

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

Crossrefs

Cf. A029793, A029795, A029800, A062397.

Cf. A011557 (a subsequence).

Programs

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