cp's OEIS Frontend

A111372 Consider the sequence defined in A083952 as a string of the digits 1 and 2. Then a(n) is the beginning position of the first occurrence of just n consecutive 1's at every other position.

%I A111372 #10 Mar 30 2012 17:31:16
%S A111372 6,0,198,170,384,992,542,648,762,5070
%N A111372 Consider the sequence defined in A083952 as a string of the digits 1 and 2. Then a(n) is the beginning position of the first occurrence of just n consecutive 1's at every other position.
%e A111372 a(0) = 6 because A083952(6) is an isolated 1,
%e A111372 a(1) = 0 because A083952(0) = A083952(2) = 1 but A083952(4) = 2,
%e A111372 a(2) = 198 because A083952(198) = A083952(200) = A083952(202) = 1, but A083952(196) = A083952(204) = 2, etc.
%t A111372 a[n_] := a[n] = Block[{s = Sum[ a[i]*x^i, {i, 0, n - 1}]}, If[ IntegerQ@ Last@ CoefficientList[ Series[ Sqrt[s + x^n], {x, 0, n}], x], 1, 2]]; t = Union@ Table[ If[ a[n] == 1, n, 0], {n, 0, 5506}]; f[n_] := Block[{k = n, m = 2}, If[n == 1, 0, While[m < Length@t && t[[m - 1]] + 2 == t[[m]] || t[[m]] + 2k != t[[m + k]] || t[[m + k]] + 2 == t[[m + k + 1]], m++ ]; If[m < Length@t - k, t[[m]], 0]]]; Table[ f[n], {n, 0, 9}]
%Y A111372 Cf. A083952, A111363.
%K A111372 nonn
%O A111372 0,1
%A A111372 _Robert G. Wilson v_, Nov 08 2005
%E A111372 Corrected and extended by _Robert G. Wilson v_, Nov 27 2006