A217186 a(n) is the number of digits in the decimal representation of the smallest power of 3 that contains n consecutive identical digits.

1, 6, 16, 16, 131, 257, 1014, 3684, 10875, 51142, 51142, 304989

Offset: 1

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base
• more

Comments

Number of digits in 3^k is equal to floor(1 + k*log_10(3)).

Crossrefs

Cf. A215727, A215733.

Programs

Mathematica

k = 0; Join[{1}, Table[While[d = IntegerDigits[3^k]; prt = Partition[Differences[d], n - 1, 1]; ! MemberQ[prt, Table[0, {n - 1}]], k++]; Length[d], {n, 2, 8}]] (* T. D. Noe, Oct 03 2012 *)

Python

def A217186(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 len(s)
        x *= 3
    return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Extensions

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