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%I #19 Jun 04 2024 11:04:03
%S 2,2,5,5,3,2,2,5,5,3,2,2,2,2,2,2,2,3,3,2,2,2,4,2,3,2,2,2,2,3,2,2,2,3,
%T 3,2,2,2,3,3,2,2,2,2,3,2,2,4,2,2,2,2,2,5,3,2,2,3,3,3,2,2,3,2,2,2,2,3,
%U 2,2,2,2,3,2,2,2,2,5,2,3,2,2,2,2,3,2,2
%N Smallest exponent k>1 such that n and n^k have some digits in common.
%C For all n, n^5-n is divisible by 10, and so n^5 == n (mod 10). Thus a(n) <= 5 for all n. - _Tom Edgar_, Jan 06 2015
%H Robert Israel, <a href="/A253600/b253600.txt">Table of n, a(n) for n = 0..10000</a>
%e For n=2, 2^k has no digit in common with 2 until k reaches 5 to give 32, hence a(2)=5.
%p f:= proc(n) local L,k;
%p L:= convert(convert(n,base,10),set);
%p for k from 2 do
%p if convert(convert(n^k,base,10),set) intersect L <> {} then
%p return k
%p fi
%p od
%p end proc:
%p map(f, [$0..100]); # _Robert Israel_, Mar 17 2020
%t seq={};Do[k=1;Until[ContainsAny[IntegerDigits[n],IntegerDigits[n^k]],k++];AppendTo[seq,k] ,{n,0,86}];seq (* _James C. McMahon_, Jun 04 2024 *)
%o (PARI) a(n) = {sd = Set(vecsort(digits(n))); k=2; while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); k;}
%Y Cf. sequences where a(n)=k: A103173 (k=5), A189056 (k=2), A253601 (k=3), A253602 (k=4).
%Y Cf. A373203.
%K nonn,base
%O 0,1
%A _Michel Marcus_, Jan 05 2015
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