%I #18 Feb 04 2024 14:14:22
%S 1,2,8,17,24,113,657,1346,3667,17318,68642,355612,355612,1678243,
%T 1678243,16207565
%N a(n) is the number of digits in the decimal representation of the smallest Lucas number that contains n consecutive identical digits.
%C Number of digits in Lucas(k) is equal to floor(1 + k*log_10((1+sqrt(5))/2)).
%t 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 (Python)
%o def A217192(n):
%o ....if n == 1:
%o ........return 1
%o ....else:
%o ........l, y, x = [str(d)*n for d in range(10)], 2, 1
%o ........for m in range(1,10**9):
%o ............s = str(x)
%o ............for k in l:
%o ................if k in s:
%o ....................return len(s)
%o ............y, x = x, y+x
%o ........return 'search limit reached'
%o # _Chai Wah Wu_, Dec 17 2014
%Y Cf. A000032, A217166, A217176.
%K nonn,base,hard
%O 1,2
%A _V. Raman_, Sep 27 2012
%E a(11) from _Chai Wah Wu_, Dec 17 2014
%E a(12)-a(16) from _Nick Hobson_, Feb 04 2024