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 A242944 #61 Jun 01 2025 12:08:15
%S A242944 3,5,7,11,37,41,43,83,269,577,1429,1433,2063,2549,8353,10639,15299,
%T A242944 16927,18637,20201,24007,30097,34039,41777,146609,394249,839203,
%U A242944 2955319
%N A242944 Primes prime(k) such that 2^k + prime(k) is also prime.
%C A242944 If instead we ask for odd primes, and therefore the index is one less than that for all primes, the sequence would begin: 3, 29, 89, 251, 659, 937, 1307, 1453, 8179, 9391, 12097, 28499, 83969, 101209, 120739, ..., .
%C A242944 If we count 1 amongst the primes (A008578), then the sequence would begin: 1, 3, 31, 71, 97, 107, 277, 307, 641, 907, 967, 1009, 1447, 3463, 3527, 7757, 8167, ..., .
%t A242944 p = 2; lst = {}; While[p < 760001, If[ PrimeQ[p + 2^PrimePi@ p], AppendTo[ lst, p]; Print@ p]; p = NextPrime@ p; c++]; lst
%t A242944 Select[Table[{n,Prime[n]},{n,3000}],PrimeQ[#[[2]]+2^#[[1]]]&][[;;,2]] (* The program generates the first 21 terms of the sequence. *) (* _Harvey P. Dale_, Mar 04 2024 *)
%Y A242944 Corresponding k are in A077375.
%Y A242944 Cf. A078583, A078686, A056206, A243428.
%K A242944 nonn,more
%O A242944 1,1
%A A242944 _Robert G. Wilson v_, Jun 20 2014
%E A242944 a(27) from _Michael S. Branicky_, May 29 2025 using A077375.
%E A242944 a(28) from _Michael S. Branicky_, Jun 01 2025