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 A194635 #37 Aug 12 2023 05:16:01
%S A194635 2,5,13,47,59,109,241,631,1109,1373,1447,16229,52267,56543,838441,
%T A194635 16935761,270704167,3296757029
%N A194635 Indices of records in A194591 restricted to prime indices.
%C A194635 Integers for which the smallest k in A194591 such that prime(n)*2^k - 1 or prime(n)*2^k + 1 is prime (A194608) increases.
%C A194635 a(19) > 10^10.
%C A194635 A194607 gives the record values of A194606.
%D A194635 Wilfrid Keller, personal communication, 2010.
%H A194635 Chris K. Caldwell, The List of Largest Known Primes, <a href="https://t5k.org/primes/page.php?id=6614">270704167 * 2^85461 - 1</a>
%H A194635 Chris K. Caldwell, The List of Largest Known Primes, <a href="https://t5k.org/primes/page.php?id=596">3296757029 * 2^191207 + 1</a>
%H A194635 Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_030.htm">Problem 30. A stepladder to B-alpha sequence</a>, The Prime Puzzles & Problems Connection.
%t A194635 l = -1; Flatten[Table[p = Prime[n]; k = 0; While[! PrimeQ[p*2^k - 1] && ! PrimeQ[p*2^k + 1], k++]; If[k > l, l = k; p, {}], {n, 10^4}]] (* _Arkadiusz Wesolowski_, Sep 04 2011 *)
%Y A194635 Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194636, A194637, A194638, A194639.
%Y A194635 Cf. A064699, A076335, A180247, A217892.
%K A194635 more,nonn
%O A194635 1,1
%A A194635 _Arkadiusz Wesolowski_, Aug 31 2011
%E A194635 a(17) was found in 2000 by Wilfrid Keller
%E A194635 a(18) was found in 2003 by Patrick De Geest
%E A194635 Edited by _Max Alekseyev_, Oct 14 2012
%E A194635 Edited by _Arkadiusz Wesolowski_, Sep 11 2013