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A272269 Numbers n such that 11^n does not contain all ten decimal digits. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 25 16:41 EDT 2019. Contains 326324 sequences. (Running on oeis4.)