A215727 a(n) is the smallest m for which 3^m contains n consecutive identical digits.

0, 11, 32, 33, 274, 538, 2124, 7720, 22791, 107187, 107187, 639226, 5756979, 8885853, 68353787, 78927180, 78927180

Offset: 1

Author

V. Raman, Aug 22 2012

Keywords

• nonn
• base
• more

Comments

3^(a(16)+1) contains exactly 16 consecutive 3's. - Bert Dobbelaere, Mar 20 2019

Examples

			3^11 = 177147, which has two digits in a row.
		

Crossrefs

Cf. A215733, A045875.

Programs

Mathematica

A215727[n_] := Module[{m = 0 , t}, t = Table[i, {i, 0, 9}, {n}];
While[True, If[ContainsAny[Subsequences[IntegerDigits[3^m], {n}], t], Return[m], m++]]; m]; Table[A215727[n], {n, 1, 14}] (* Robert Price, Oct 16 2018 *)

Python

def A215727(n):
    l, x = [str(d)*n for d in range(10)], 1
    for m in range(10**9):
        s = str(x)
        for k in l:
            if k in s:
                return m
        x *= 3
    return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Extensions

a(12) from Chai Wah Wu, Dec 17 2014

a(13)-a(14) from Giovanni Resta, Apr 20 2016

a(15) from Bert Dobbelaere, Mar 04 2019

a(16)-a(17) from Bert Dobbelaere, Mar 20 2019