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

1,3

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.

Links

Table of n, a(n) for n=1..29.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A001020, A030706, A130696, A171102.

Sequence in context: A032517 A246087 A246094 * A250394 A062996 A085380

Adjacent sequences: A272266 A272267 A272268 * A272270 A272271 A272272

Keyword

nonn,base

Author

Altug Alkan, Apr 24 2016

Status

approved