A217157 a(n) is the least value of k such that the decimal expansion of n^k contains two consecutive identical digits.

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

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