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A253644 Numbers n such that n^k is zeroless for k=0,...,5.

%I A253644 #11 Sep 07 2018 17:43:15
%S A253644 1,2,3,5,6,13,14,17,23,24,26,31,58,62,66,68,72,76,88,96,137,168,188,
%T A253644 233,244,262,264,296,337,376,382,383,483,488,511,514,518,519,582,628,
%U A253644 719,736,786,816,822,928,938,971,978,1122,1178,1291,1331,1392,1413,1414,1663,1777
%N A253644 Numbers n such that n^k is zeroless for k=0,...,5.
%C A253644 A subsequence of A252484 (analog for k <= 4) which contains A253647 (analog including k = 6) as a subsequence. Primes in this sequence are listed in A253645.
%C A253644 Conjectured to be finite.
%H A253644 Giovanni Resta, <a href="/A253644/b253644.txt">Table of n, a(n) for n = 1..10000</a>
%p A253644 filter:= proc(x)
%p A253644   local k;
%p A253644   for k from 1 to 5 do
%p A253644     if has(convert(x^k,base,10),0) then return false fi
%p A253644   od:
%p A253644   true
%p A253644 end proc:
%p A253644 select(filter, [$1..10000]); # _Robert Israel_, Jan 07 2015
%t A253644 Select[Range[2000],Count[Flatten[IntegerDigits/@(#^Range[5])],0]==0&] (* _Harvey P. Dale_, Jun 10 2017 *)
%o A253644 (PARI) is_A253644(n,K=5)=!forstep(k=K,1,-1,vecmin(digits(n^k))||return)
%Y A253644 Cf. A052382, A104264, A124648, A124649, A253645, A253646, A253647.
%K A253644 nonn,base
%O A253644 1,2
%A A253644 _M. F. Hasler_, Jan 07 2015