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

1,2

Comments

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

Links

Table of n, a(n) for n=1..12.

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 *)

Prog

(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

Crossrefs

Cf. A215727, A215733.

Sequence in context: A222884 A230949 A231023 * A101239 A242331 A335226

Adjacent sequences: A217183 A217184 A217185 * A217187 A217188 A217189

Keyword

nonn,base,more

Author

V. Raman, Sep 27 2012

Extensions

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

Status

approved