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

%I A217191 #21 Mar 12 2025 18:44:05
%S A217191 1,2,10,14,25,185,460,1357,13027,28264,73895,242950,1077514,1521516,
%T A217191 7806974
%N A217191 a(n) is the number of digits in the decimal representation of the smallest Fibonacci number that contains n consecutive identical digits.
%C A217191 Number of digits in Fibonacci(k) is equal to floor(1 + k*log_10((1+sqrt(5))/2)-log_10(sqrt(5))).
%t A217191 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 *)
%o A217191 (Python)
%o A217191 def A217191(n):
%o A217191     if n == 1:
%o A217191         return 1
%o A217191     else:
%o A217191         l, y, x = [str(d)*n for d in range(10)], 0, 1
%o A217191         for m in range(1, 10**9):
%o A217191             s = str(x)
%o A217191             for k in l:
%o A217191                 if k in s:
%o A217191                     return len(s)
%o A217191             y, x = x, y+x
%o A217191         return 'search limit reached'
%o A217191 # _Chai Wah Wu_, Dec 17 2014
%Y A217191 Cf. A000045, A217165, A217175.
%K A217191 nonn,base,hard
%O A217191 1,2
%A A217191 _V. Raman_, Sep 27 2012
%E A217191 a(10)-a(11) from _Chai Wah Wu_, Dec 17 2014
%E A217191 a(12)-a(15) from _Nick Hobson_, Feb 15 2024