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 A082862 #21 Aug 10 2024 10:50:43
%S A082862 2,19,131,311,1619,3671,1742537,148948139,2777105129,16149760533341,
%T A082862 10082409897709157
%N A082862 Prime(2^j) where j are the positions at which (prime(2^k+1)-prime(2^k))/log(prime(2^k)) set low-value records.
%C A082862 Similar to but not identical to A074327.
%H A082862 American Institute of Mathematics, <a href="https://web.archive.org/web/20130529134247/http://www.aimath.org:80/release_goldston.html">San Jose State Math Researcher Experiences Epiphany at American Institute Of Mathematics</a>, March 21, 2003. [Wayback Machine link]
%H A082862 American Institute of Mathematics, <a href="https://web.archive.org/web/20050605085125/http://aimath.org:80/goldston_tech/">Small gaps between consecutive primes</a>. [Wayback Machine link]
%H A082862 American Institute of Mathematics, <a href="https://web.archive.org/web/20050420220143/http://www.aimath.org/primegaps/residueerror/">On the error in Goldston and Yildirim's "Small gaps between consecutive primes"</a>. [Wayback Machine link]
%e A082862 The values of quotients at primes of this sequence are as follows: 1.442695..., 1.358493..., 1.230719..., 0.348444..., 0.270651..., 0.243658..., 0.139170..., 0.106274..., 0.091976..., 0.065761..., 0.054274... .
%t A082862 q=4; Do[s=(Prime[2^n+1]-Prime[2^n])/Log[Prime[2^n]]//N; If[s<q, Print[{Prime[2^n], s}]; q=s], {n, 0, 30}] (* corrected by _Amiram Eldar_, Aug 10 2024 *)
%Y A082862 Cf. A033844, A051439, A074327.
%K A082862 nonn,hard,more
%O A082862 1,1
%A A082862 _Labos Elemer_, Apr 14 2003
%E A082862 Data corrected and extended by _Amiram Eldar_, Aug 10 2024