This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111363 #6 Mar 30 2012 18:36:50
%S A111363 1,3,7,11,13,27,31,33,37,51,53,57,61,63,127,131,133,137,151,153,161,
%T A111363 165,167,171,173,175,177,181,185,193,195,199,201,203,215,217,221,227,
%U A111363 229,231,235,237,241,243,245,261,263,265,273,275,279,283,287,289,291,295
%N A111363 a(n) = A108783(n) + 1.
%C A111363 Positions of the 1's in A083952 but indexing that sequence starting at 1. A108783 is the preferred version.
%F A111363 It appears that a(n)~4.1*n.
%t A111363 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]; Position[ Table[a[n], {n, 0, 300}], 1] // Flatten
%Y A111363 Cf. A083952. See A108783 for another version.
%K A111363 nonn
%O A111363 1,2
%A A111363 _Paul D. Hanna_ and _Robert G. Wilson v_, Nov 08 2005