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A217157 a(n) is the least value of k such that the decimal expansion of n^k contains two consecutive identical digits. 7
16, 11, 8, 11, 5, 6, 6, 6, 2, 1, 2, 9, 3, 2, 4, 7, 5, 5, 2, 2, 1, 6, 4, 6, 5, 4, 8, 5, 2, 6, 5, 1, 2, 2, 3, 7, 2, 4, 2, 5, 3, 4, 1, 3, 2, 2, 3, 3, 2, 7, 4, 3, 6, 1, 4, 4, 2, 4, 2, 3, 2, 3, 3, 2, 1, 2, 3, 4, 2, 3, 7, 6, 3, 6, 2, 1, 3, 4, 2, 3, 3, 2, 5, 2, 4, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Least number m such that n^m is a term of A171901 - Chai Wah Wu, Feb 20 2019

Conjecture: 1 <= a(n) <= 16 for n > 1 and a(n) < 16 for n > 2. - Chai Wah Wu, Feb 20 2019

a(n) >= 1 for all n > 1 and is bounded: see link for proof. - Robert Israel, Feb 21 2019

LINKS

V. Raman, Table of n, a(n) for n = 2..10000

Robert Israel, Proof that A217157 >= 1 and is bounded

FORMULA

a(A171901(n)) = 1. - Chai Wah Wu, Feb 20 2019

a(n) = A215236(n) + 1. - Georg Fischer, Nov 25 2020

MAPLE

f:= proc(n) local L, k;

   for k from 1 do

      L:= convert(n^k, base, 10);

      if has(L[2..-1]-L[1..-2], 0) then return k fi

   od

end proc:

map(f, [$2..100]); # Robert Israel, Feb 21 2019

MATHEMATICA

Table[k = 1; While[! MemberQ[Differences[IntegerDigits[n^k]], 0], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)

PROG

Python)

def A217157(n):

    m, k = 1, n

    while True:

       s = str(k)

       for i in range(1, len(s)):

         if s[i] == s[i-1]:

            return m

       m += 1

       k *= n # Chai Wah Wu, Feb 20 2019

CROSSREFS

Cf. A045875, A215236.

Cf. A215727, A215728, A215729, A215730, A215731, A171901, A306305.

Sequence in context: A040242 A306378 A232999 * A070578 A225842 A298450

Adjacent sequences:  A217154 A217155 A217156 * A217158 A217159 A217160

KEYWORD

nonn,base

AUTHOR

V. Raman, Sep 27 2012

STATUS

approved

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Last modified October 23 19:26 EDT 2021. Contains 348215 sequences. (Running on oeis4.)