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%I #23 Feb 03 2024 10:16:14
%S 0,5,36,78,112,538,3139,6436,17544,82864,328448,1701593,1701593,
%T 8030342,8030342,77552742
%N a(n) is the least value of k such that the decimal expansion of Lucas(k) contains n consecutive identical digits.
%C a(12) > 1512000. - _Chai Wah Wu_, Dec 17 2014
%C a(17) > 10^8. - _Nick Hobson_, Feb 02 2024
%H Nick Hobson, <a href="/A217166/a217166.c.txt">C program</a>
%t 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 (Python)
%o def A217166(n):
%o ....if n == 1:
%o ........return 0
%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 m
%o ............y, x = x, y+x
%o ........return 'search limit reached'
%o # _Chai Wah Wu_, Dec 17 2014
%o (C) See Links section.
%Y Cf. A000032, A045875, A215727, A215728, A215729, A215730, A215731.
%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 02 2024
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