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 A265104 #14 Dec 04 2015 01:42:10
%S A265104 8,26,35,80,89,107,116,242,251,269,278,323,332,350,359,728,737,755,
%T A265104 764,809,818,836,845,971,980,998,1007,1052,1061,1079,1088,2186,2195,
%U A265104 2213,2222,2267,2276,2294,2303,2429,2438,2456,2465,2510,2519,2537
%N A265104 a(n) = A265100(n+1) - 6, n >= 1.
%C A265104 In the following, let "gap" and "gap number" be as defined in A265100, and let C(m) denote the m-th Catalan number (A000108).
%C A265104 Conjecture 1: The sequence contains all possible gap numbers.
%C A265104 Conjecture 2: For any gap G, the order |G| of G is the constant |G| = 6.
%C A265104 Conjecture 3: If g is a gap number, then 3*g + 2 is a gap number.
%C A265104 Conjecture 4: If C(m) =!= 0 (mod 3), then C(3*m+1) =!= 0 (mod 3) (=!= means "not congruent") or, what is the same thing, if m lies in a gap, then 3*m + 1 lies in a gap.
%F A265104 a(n) = (3^(A007814(n) + 2) - 3)/2 + A265100(2^(A007814(n))*(2*A003602(n) - 1)), n >= 1.
%F A265104 Conjecture: a(n) = A265100(n) + A085296(n).
%t A265104 a005836[1] := 0; a005836[n_] := If[OddQ[n], 3*a005836[Floor[(n + 1)/2]], a005836[n - 1] + 1]; a265100[n_] := 9*a005836[n] + 5; a265104[n_] := a265100[n+1] - 6; Table[a265104[n], {n, 46}]
%t A265104 (* Or: *)
%t A265104 a007814[x_] := IntegerExponent[x, 2]; a003602[x_] := (1 + x/2^a007814[x])/2; a005836[1] := 0; a005836[n_] := If[OddQ[n], 3*a005836[Floor[(n + 1)/2]], a005836[n - 1] + 1]; a265100[n_] := 9*a005836[n] + 5; a265104[n_] := (3^(a007814[n] + 2) - 3)/2 + a265100[2^(a007814[n])*(2*a003602[n] - 1)]; Table[a265104[n], {n, 46}]
%Y A265104 Cf. A265100.
%K A265104 nonn
%O A265104 1,1
%A A265104 _L. Edson Jeffery_, Dec 01 2015