A217191 a(n) is the number of digits in the decimal representation of the smallest Fibonacci number that contains n consecutive identical digits.

1, 2, 10, 14, 25, 185, 460, 1357, 13027, 28264, 73895, 242950, 1077514, 1521516, 7806974

Offset

1,2

Comments

Number of digits in Fibonacci(k) is equal to floor(1 + k*log_10((1+sqrt(5))/2)-log_10(sqrt(5))).

Links

Table of n, a(n) for n=1..15.

Mathematica

k = 0; Join[{1}, Table[While[d = IntegerDigits[Fibonacci[k]]; ! MemberQ[Partition[Differences[d], n - 1, 1], Table[0, {n - 1}]], k++]; Length[d], {n, 2, 8}]] (* T. D. Noe, Oct 02 2012 *)

Prog

(Python)
def A217191(n):
....if n == 1:
........return 1
....else:
........l, y, x = [str(d)*n for d in range(10)], 0, 1
........for m in range(1, 10**9):
............s = str(x)
............for k in l:
................if k in s:
....................return len(s)
............y, x = x, y+x
........return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Crossrefs

Cf. A000045, A217165, A217175.

Sequence in context: A230624 A290143 A160773 * A190043 A217681 A102340

Adjacent sequences: A217188 A217189 A217190 * A217192 A217193 A217194

Keyword

nonn,base,hard

Author

V. Raman, Sep 27 2012

Extensions

a(10)-a(11) from Chai Wah Wu, Dec 17 2014

a(12)-a(15) from Nick Hobson, Feb 15 2024

Status

approved