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 A109835 #15 Apr 03 2023 10:36:10 %S A109835 3,37,157,661,877,997,1237,1657,2137,2557,3061,4177,4261,4357,4621, %T A109835 5581,6037,6121,6217,6361,7537,8317,8461,8521,9241,9277,9721,9901, %U A109835 10837,11497,12241,12421,13417,13681,14737,14821,15121,15277,16417,17257 %N A109835 Primes connected to two primes by the (p+1)/2 and 2p-1 operators. %C A109835 Primes involved in Cunningham chains of the second kind (2p-1) and not starting or ending them. A059455 is produced by the same rule, but "of the first kind (2p+1)". %H A109835 Chris Caldwell's Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chains</a>. %e A109835 a(2)=37 is here because (37 + 1)/2 = 19 and 2*37 - 1 = 73 are both primes; %e A109835 a(11)=3061 because 1531 -> 3061 -> 6121 through <2p-1> and all are primes; %e A109835 a(11)=3061, a(18)=6121 and a(31)=12241 are here because they are inside the complete Cunningham chain of the second kind 1531 -> 3061 -> 6121 -> 12241 -> 24481. %t A109835 Select[Prime[Range[5000]],PrimeQ[(#+1)/2]&&PrimeQ[2#-1]&] (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2010 *) %Y A109835 Cf. A059455, A005385. %K A109835 nonn %O A109835 1,1 %A A109835 _Alexandre Wajnberg_, Aug 31 2005