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 A227126 #56 May 31 2025 19:54:04
%S A227126 2,3,5,11,17,167,193,197,433,4111,9173,42929,95279,98897,139409,
%T A227126 142567,228617,329333,344209,791191,829177,1274509,1284037,2432791,
%U A227126 2443741
%N A227126 Primes prime(k) such that 2^(k+1) - prime(k) is also prime.
%C A227126 The corresponding primes 2^(k + 1) - prime(k) are 2, 5, 11, 53, 239, 1099511627609, 35184372088639, ...
%C A227126 The prime indices k are 1, 2, 3, 5, 7, 39, 44, 45, 84, 566, 1137, ...
%e A227126 5 is a term because 5 is the 3rd prime, and 2^(3+1) - 5 = 16 - 5 = 11 which is a prime
%e A227126 11 is in the sequence because 11 = prime(5) and 2^(5 + 1) - 11 = 64 - 11 = 53 is a prime.
%t A227126 p = 2; lst = {}; While[p < 850001, If[ PrimeQ[ 2^(PrimePi@ p +1) - p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst (* _Robert G. Wilson v_, Jul 09 2014 *)
%o A227126 (PARI) lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip+1)-p), print1(p, ", ")); ip++;);} \\ _Michel Marcus_, Jul 12 2014
%Y A227126 Cf. A078686, A244913, A244916, A242944, A228021.
%K A227126 nonn,more
%O A227126 1,1
%A A227126 _Gerasimov Sergey_, Jul 02 2013
%E A227126 a(3), a(6), a(8)-a(12) from _Joerg Arndt_, Jul 03 2013
%E A227126 Corrected and extended through a(21) by _Robert G. Wilson v_, Jul 09 2014
%E A227126 Entry revised by _N. J. A. Sloane_, Jan 02 2019, incorporating data from a later submission from _Robert G. Wilson v_
%E A227126 a(22)-a(25) from _Michael S. Branicky_, May 31 2025