A217192 - OEIS

%I #25 Feb 25 2026 14:40:15

%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, A217191.

%K nonn,base,hard,more

%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