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 A124165 #19 Sep 17 2024 04:45:13
%S A124165 7,17,89,1223,5479,11257,11519,12583,23081,36479,52567,52919,125929,
%T A124165 365689,1127239,1148729,4533073
%N A124165 Primes p such that (2^p + 2^((p+1)/2) + 1)/5 is prime.
%C A124165 PrimePi[ a(n) ] = {4, 7, 24, 200, 724, 1361, 1389, 1503, 2578, 3868, 5368, 5400, 11814, 31200, ...}.
%C A124165 3 terms found by _David Broadhurst_ in Nov 2006: {36479, 52567, 52919}.
%C A124165 Only 2 terms found by Jean Penne in Nov 2006 belong to a(n): {125929, 365689}.
%C A124165 5 other numbers found by Jean Penne in Nov 2006 belong to related sequence of primes p such that (2^p - 2^((p+1)/2) + 1)/5 is prime: {221891, 235099, 305867, 311027, 333227}.
%C A124165 All terms belong to A124112 = {5, 7, 9, 11, 13, 17, 29, 43, 53, 89, 283, 557, 563, 613, 691, 1223, 2731, ...} (numbers k such that ((1+i)^k+1)/(2+i) is a Gaussian prime).
%C A124165 The terms 1127239 and 1148729 were found by Borys Jaworski in 2006-2007. - _Alexander Adamchuk_, Jun 20 2007
%H A124165 Henri Lifchitz and Renaud Lifchitz: <a href="http://www.primenumbers.net/prptop/prptop.php">PRP Records. Probable Primes Top 10000</a>.
%t A124165 Do[p=Prime[n];f=(2^p+2^((p+1)/2)+1)/5;If[PrimeQ[f],Print[{n,p}]],{n,1,200}]
%Y A124165 Cf. A124112 (numbers k such that ((1+i)^k+1)/(2+i) is a Gaussian prime).
%K A124165 hard,more,nonn
%O A124165 1,1
%A A124165 _Alexander Adamchuk_, Dec 02 2006, Dec 04 2006
%E A124165 a(17) from _Serge Batalov_, Mar 31 2014