cp's OEIS Frontend

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

%I A029797 #23 Nov 20 2023 11:54:06
%S A029797 0,1,10,100,146,1000,1203,1460,7652,8077,8751,8965,10000,10406,11914,
%T A029797 12030,12057,12586,12768,12961,13055,14202,14600,14625,16221,19350,
%U A029797 20450,21539,22040,22175,23682,24071,25089,25201,25708,26653,26981
%N A029797 Numbers k such that k^2 and k^3 have the same set of digits.
%C A029797 Conjecture: there exists some m and N for which a(n) = m + n for all n >= N. [_Charles R Greathouse IV_, Jun 28 2011]
%C A029797 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
%H A029797 Charles R Greathouse IV, <a href="/A029797/b029797.txt">Table of n, a(n) for n = 1..10000</a>
%e A029797 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
%o A029797 (Magma) [ n: n in [0..34*10^4] | Set(Intseq(n^2)) eq Set(Intseq(n^3)) ];  // _Bruno Berselli_, Jun 28 2011
%o A029797 (PARI) isA029797(n)=Set(Vec(Str(n^2)))==Set(Vec(Str(n^3))) \\ _Charles R Greathouse IV_, Jun 28 2011
%Y A029797 Cf. A029793, A029795, A029800, A062397.
%Y A029797 Cf. A011557 (a subsequence).
%K A029797 nonn,base
%O A029797 1,3
%A A029797 _Patrick De Geest_