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%I #36 May 18 2017 20:36:23
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,25,27,28,
%T 34,38,41
%N Numbers n such that 11^n does not contain all ten decimal digits.
%C Inspiration was the simple form of 11 that is concatenation of 1 and 1. With similar motivation, A130696 focuses on the values of 2^n = (1 + 1)^n. Since this sequence exists in base 10, 11^n*10 is simply concatenation of 11^n and 0. So 11^(n+1) = concat(11^n, 0) + 11^n while 2^(n+1) = 2^n + 2^n.
%C A030706 is a subsequence. So note that if there is currently no proof of finiteness of A030706, then there is no proof yet of the finiteness of this sequence.
%e 25 is a term because 11^25 = 108347059433883722041830251 that does not contain digit 6.
%e 26 is not a term because 11^26 = 11^25*10 + 11^25 = 1083470594338837220418302510 + 108347059433883722041830251 = 1191817653772720942460132761 that contains all ten decimal digits.
%t Select[Range[0, 120], AnyTrue[DigitCount[11^#], # == 0 &] &] (* _Michael De Vlieger_, Apr 24 2016, Version 10 *)
%o (PARI) isA171102(n) = 9<#vecsort(Vecsmall(Str(n)), , 8);
%o lista(nn) = for(n=0, nn, if(!isA171102(11^n), print1(n, ", ")));
%o (PARI) select( is_A272269(n)=#Set(digits(11^n))<10 ,[0..100]) \\ _M. F. Hasler_, May 18 2017
%Y Cf. A001020, A030706, A130696, A171102.
%K nonn,base
%O 1,3
%A _Altug Alkan_, Apr 24 2016
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