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 A174217 #13 Jan 29 2019 04:36:02
%S A174217 7,13,31,61,139,283,571,1153,2311,4723,9463,19141,38569,77419,154873,
%T A174217 310231,620911,1241923,2483869,4967803,9946273,19892599
%N A174217 a(n) = (A174216(n)-1)/2.
%C A174217 Related to the generation of twin primes according to section 6 of the preprint.
%H A174217 V. Shevelev, <a href="http://arXiv.org/abs/0912.4006">Theorems on twin primes-dual case</a>, arXiv:0912.4006 [math.GM], 2009-2014.
%F A174217 A174214(A174216(n)) = 3*a(n), n>1.
%t A174217 (* b = A174214 *) b[n_] := b[n] = Which[n == 9, 14, CoprimeQ[b[n - 1], n - 1 - (-1)^n], b[n - 1] + 1, True, 2 n - 4];
%t A174217 (* c = A174216 *) c[n_] := c[n] = If[n == 1, 15, For[k = c[n - 1] + 1, True, k++, If[2 b[k] == 3 (k - 1), Return[k]]]];
%t A174217 Table[a[n] = (c[n] - 1)/2; Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 22}] (* _Jean-François Alcover_, Jan 29 2019 *)
%Y A174217 Cf. A174214, A174215, A174216, A166945, A167495.
%K A174217 nonn,more
%O A174217 1,1
%A A174217 _Vladimir Shevelev_, Mar 12 2010
%E A174217 Terms after a(11) corrected by _Vladimir Shevelev_, Nov 02 2010