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%I #5 Apr 19 2013 22:25:58
%S 1,2,1,2,1,2,12,22,1,1,4,4,1,2,1,3,2,2,11,1,202,1,5,1,2,1,5,1,2,1,1,1,
%T 1,3,2,1,2,2,5,2,1,1,2,1,3,1,1,15,2,1,12,1,2,2,1,1,1,2,1,3,1,2,10,1,6,
%U 5,1,2,1,2,6,1,1,2,8,2,19,3,1,1,1,2,1,1,1,5,1,2,2,1,3,1,6,12,2,4,1,5,1,2,4
%N Continued fraction expansion of the constant given by Sum_{n>=0} A083952(n)/2^(n+1).
%t a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/2), {x, 0, l}], x]]] != True, k++ ]; k]; t = Table[a[n], {n, 0, 370}]; ContinuedFraction[ FromDigits[{t - 1, 0}, 2]]
%Y Cf. A083952, A113737.
%K base,nonn
%O 0,2
%A _Robert G. Wilson v_, Nov 08 2005
%E Entry revised by _Paul D. Hanna_, Apr 19 2013