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%I #9 Jul 15 2015 09:09:22
%S 1,2,3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,21,23,24,25,26,27,28,29,31,
%T 35,36,38,39,41,44,46,54,56,57,58,61,62,65,66,68,72,75,76,77,81,82,83,
%U 85,88,91,92,96,111,113,114,119,121,122,125,129,132,133,136,137,139,146,154,156,157,158,161
%N Numbers n such that n^k is zeroless for k=0,...,3.
%C See A252484 for the subsequence of numbers having this property up to k=4.
%t Select[Range[200],AllTrue[#^Range[3],DigitCount[#,10,0]==0&]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 15 2015 *)
%o (PARI) is_A253643(n,K=3)=!forstep(k=K,1,-1,vecmin(digits(n^k))||return)
%o (Python)
%o for n in range(100):
%o ..s1,s2,s3 = str(n),str(n**2),str(n**3)
%o ..if s1.find('0') + s2.find('0') + s3.find('0') == -3:
%o ....print(n,end=', ') # _Derek Orr_, Mar 09 2015
%Y Cf. A052382, A252484 (k <= 4), A253644 (k <= 5), A253645 (primes, k <= 5), A253647 (k <= 6), A253646 (primes, k <= 6), A124648 (k <= 7), A124649 (k <= 8).
%Y Cf. A104264.
%K nonn,base,easy
%O 1,2
%A _M. F. Hasler_, Mar 09 2015
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