A272269 Numbers n such that 11^n does not contain all ten decimal digits.

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, 34, 38, 41

Offset: 1

Author

Altug Alkan, Apr 24 2016

Keywords

• nonn
• base

Comments

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.

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.

Examples

			25 is a term because 11^25 = 108347059433883722041830251 that does not contain digit 6.
26 is not a term because 11^26 = 11^25*10 + 11^25 = 1083470594338837220418302510 + 108347059433883722041830251 = 1191817653772720942460132761 that contains all ten decimal digits.
		

Crossrefs

Cf. A001020, A030706, A130696, A171102.

Programs

Mathematica

Select[Range[0, 120], AnyTrue[DigitCount[11^#], # == 0 &] &] (* Michael De Vlieger, Apr 24 2016, Version 10 *)

PARI

isA171102(n) = 9<#vecsort(Vecsmall(Str(n)), , 8);
lista(nn) = for(n=0, nn, if(!isA171102(11^n), print1(n, ", ")));

PARI

select( is_A272269(n)=#Set(digits(11^n))<10 ,[0..100]) \\ M. F. Hasler, May 18 2017