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 A096475 #27 Feb 14 2025 03:42:29
%S A096475 3,17,11,41,71,101,29,569,881,137,1151,521,1289,2027,10331,1229,3461,
%T A096475 461,2549,2129,6569,6131,14387,34157,5657,4259,44621,17387,25301,
%U A096475 11159,56099,34367,64877,23201,80147,73361,21017,46349,162287,94439,469877,122501,35507
%N A096475 a(n) is the smallest lesser of twin prime p, such that prime(2 + p) - prime(p) = 2n (cf. A096474).
%H A096475 Amiram Eldar, <a href="/A096475/b096475.txt">Table of n, a(n) for n = 3..202</a>
%F A096475 a(n) = min{x; A096474(x) = 2n} for n = 3, 4, ...
%t A096475 {ta = Table[0, {1300}], tb = Table[0, {1300}], tc = Table[0, {1300}], u = 1}; Do[s = Prime[n + 1] - Prime[n]; If[s == 2, ta[[u]] = Prime[Prime[n + 1]] - Prime[Prime[n]]; tb[[u]] = n; tc[[u]] = Prime[n]; u = u + 1], {n, 1, 10000}]; a[n_] := tc[[FirstPosition[ta, 2 n][[1]]]]; Table[a[n], {n, 3, 40}] (* _Jean-François Alcover_, Jul 28 2017, using Mathematica code for A096464 *)
%o A096475 (PARI) a(n) = {forprime(p=3, , if (isprime(p+2) && (prime(2+p)-prime(p) == 2*n), return (p))); p=3;} \\ _Michel Marcus_, Jul 28 2017
%o A096475 (PARI) list(len) = {my(v = vector(len), c = 0, q = 2, p1 = 2, p2 = 3, i); forprime(p3 = 5, , q++; if(isprime(q) && isprime(q-2), i = (p3-p1)/2 - 2; if(i <= len && v[i]==0, v[i] = q-2; c++; if(c == len, break))); p1 = p2; p2 = p3); v;} \\ _Amiram Eldar_, Feb 14 2025
%Y A096475 Cf. A001359, A096474, A096476.
%K A096475 nonn
%O A096475 3,1
%A A096475 _Labos Elemer_, Jun 23 2004
%E A096475 Name edited by _Michel Marcus_, Jul 28 2017
%E A096475 a(41)-a(45) from _Michel Marcus_, Jul 28 2017