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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
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)).
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
Sequence in context: A222884 A230949 A231023 * A101239 A242331 A335226
KEYWORD
nonn,base,more
AUTHOR
V. Raman, Sep 27 2012
EXTENSIONS
a(12) from Chai Wah Wu, Dec 17 2014
STATUS
approved