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A215731 a(n) is the smallest m for which the decimal representation of 11^m contains n consecutive identical digits.

%I A215731 #46 Oct 04 2024 00:24:35
%S A215731 0,1,8,39,156,482,1323,2983,9443,39879,214747,296095,296095,5541239,
%T A215731 8621384,30789328
%N A215731 a(n) is the smallest m for which the decimal representation of 11^m contains n consecutive identical digits.
%e A215731 The decimal representation of 11^39879 contains ten consecutive 6s, and is the least such power with such a string of digits.
%t A215731 mostDigits[t_] := Module[{lastDigit = t[[1]], record = 1, cnt = 1}, Do[If[t[[n]] == lastDigit, cnt++, If[cnt > record, record = cnt]; cnt = 1; lastDigit = t[[n]]], {n, 2, Length[t]}]; If[cnt > record, record = cnt] ; record]; nn = 10; t = Table[-1, {nn}]; n = -1; While[Min[t] == -1, n++; c = mostDigits[IntegerDigits[11^n]]; If[c > nn, c = nn]; While[c > 0 && t[[c]] == -1, t[[c]] = n; c--]]; t (* _T. D. Noe_, Apr 29 2013 *)
%o A215731 (Python)
%o A215731 def A215731(n):
%o A215731     l, x = [str(d)*n for d in range(10)], 1
%o A215731     for m in range(10**9):
%o A215731         s = str(x)
%o A215731         for k in l:
%o A215731             if k in s:
%o A215731                 return m
%o A215731         x *= 11
%o A215731     return 'search limit reached'
%o A215731 # _Chai Wah Wu_, Dec 17 2014
%Y A215731 Cf. A215737 (the repeated digits), A045875, A215727, A215728, A215729, A215730.
%K A215731 nonn,base,more
%O A215731 1,3
%A A215731 _V. Raman_, Aug 22 2012
%E A215731 a(10) discovered by "Wick" (See http://www.mersenneforum.org/showpost.php?p=334789&postcount=89).  Definition clarified and all terms to a(10) verified by _Daran Gill_, Mar 24 2013
%E A215731 a(11) discovered by Tom Womack (See http://www.mersenneforum.org/showpost.php?p=337916&postcount=105), _Rick van der Hoorn_, Apr 24 2013
%E A215731 a(12)-a(13) from _Giovanni Resta_, Apr 25 2013
%E A215731 Corrected a(12), _Rick van der Hoorn_, Apr 28 2013
%E A215731 a(14) from _Giovanni Resta_, Apr 18 2016
%E A215731 a(15) from _Bert Dobbelaere_, Feb 15 2019
%E A215731 a(16) from _Paul Geneau de Lamarlière_, Oct 03 2024