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A217192 a(n) is the number of digits in the decimal representation of the smallest Lucas number that contains n consecutive identical digits.

%I A217192 #22 Mar 12 2025 20:15:05
%S A217192 1,2,8,17,24,113,657,1346,3667,17318,68642,355612,355612,1678243,
%T A217192 1678243,16207565
%N A217192 a(n) is the number of digits in the decimal representation of the smallest Lucas number that contains n consecutive identical digits.
%C A217192 Number of digits in Lucas(k) is equal to floor(1 + k*log_10((1+sqrt(5))/2)).
%t A217192 k = 0; Join[{1}, Table[While[d = IntegerDigits[LucasL[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 A217192 (Python)
%o A217192 def A217192(n):
%o A217192     if n == 1:
%o A217192         return 1
%o A217192     else:
%o A217192         l, y, x = [str(d)*n for d in range(10)], 2, 1
%o A217192         for m in range(1, 10**9):
%o A217192             s = str(x)
%o A217192             for k in l:
%o A217192                 if k in s:
%o A217192                     return len(s)
%o A217192             y, x = x, y+x
%o A217192         return 'search limit reached'
%o A217192 # _Chai Wah Wu_, Dec 17 2014
%Y A217192 Cf. A000032, A217166, A217176.
%K A217192 nonn,base,hard
%O A217192 1,2
%A A217192 _V. Raman_, Sep 27 2012
%E A217192 a(11) from _Chai Wah Wu_, Dec 17 2014
%E A217192 a(12)-a(16) from _Nick Hobson_, Feb 04 2024