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A217166 a(n) is the least value of k such that the decimal expansion of Lucas(k) contains n consecutive identical digits.

%I A217166 #26 Mar 12 2025 18:41:50
%S A217166 0,5,36,78,112,538,3139,6436,17544,82864,328448,1701593,1701593,
%T A217166 8030342,8030342,77552742
%N A217166 a(n) is the least value of k such that the decimal expansion of Lucas(k) contains n consecutive identical digits.
%C A217166 a(12) > 1512000. - _Chai Wah Wu_, Dec 17 2014
%C A217166 a(17) > 10^8. - _Nick Hobson_, Feb 02 2024
%H A217166 Nick Hobson, <a href="/A217166/a217166.c.txt">C program</a>
%t A217166 k = 0; Join[{0}, Table[While[d = IntegerDigits[LucasL[k]]; ! MemberQ[Partition[Differences[d], n - 1, 1], Table[0, {n - 1}]], k++]; k, {n, 2, 8}]] (* _T. D. Noe_, Oct 02 2012 *)
%o A217166 (Python)
%o A217166 def A217166(n):
%o A217166     if n == 1:
%o A217166         return 0
%o A217166     else:
%o A217166         l, y, x = [str(d)*n for d in range(10)], 2, 1
%o A217166         for m in range(1, 10**9):
%o A217166             s = str(x)
%o A217166             for k in l:
%o A217166                 if k in s:
%o A217166                     return m
%o A217166             y, x = x, y+x
%o A217166         return 'search limit reached'
%o A217166 # _Chai Wah Wu_, Dec 17 2014
%o A217166 (C) // See Links section.
%Y A217166 Cf. A000032, A045875, A215727, A215728, A215729, A215730, A215731.
%K A217166 nonn,base,hard
%O A217166 1,2
%A A217166 _V. Raman_, Sep 27 2012
%E A217166 a(11) from _Chai Wah Wu_, Dec 17 2014
%E A217166 a(12)-a(16) from _Nick Hobson_, Feb 02 2024