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Numbers n such that n and n^5 have the same set of digits.
3

%I #12 Sep 08 2022 08:46:06

%S 0,1,10,100,1000,10000,39568,100000,395680,1000000,2114325,2751490,

%T 3246105,3956800,4356891,4768209,4926051,6274019,8021439,10000000,

%U 10267394,10352849,10368279,10456932,10478632,10489723,10489725,10527934,10567293,10639428,10827439

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

%H Lars Blomberg, <a href="/A232660/b232660.txt">Table of n, a(n) for n = 1..10000</a>

%H B. Avila and T. Khovanova, <a href="http://arxiv.org/abs/1403.4614">Free Fibonacci Sequences</a>, arXiv preprint arXiv:1403.4614, 2014

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

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

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

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

%K nonn,base

%O 1,3

%A _Arkadiusz Wesolowski_, Nov 27 2013