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 A301634 #52 Jun 23 2024 07:16:24
%S A301634 0,1,5,13,65,85,229,2005,3875,3919,5417,8819,11899,16668,19445,28242,
%T A301634 33407,37918,40594,141251
%N A301634 Numbers k such that 2^k + 2*k + 1 is prime.
%C A301634 Next term, if it exists, is greater than 50000. Terms up to 229 correspond to provable primes. The terms greater than or equal to 2005 correspond to probable primes. - _Jon E. Schoenfield_ and _Vaclav Kotesovec_, Mar 27 2018
%p A301634 a:=k->`if`(isprime(2^k+2*k+1),k,NULL): seq(a(k),k=0..6000); # _Muniru A Asiru_, Mar 25 2018
%t A301634 Flatten[{0, Select[Range[5000], PrimeQ[2^# + 2*# + 1] &]}] (* _Vaclav Kotesovec_, Mar 25 2018 *)
%o A301634 (PARI) for(n=0, 500, if(isprime(2^n+2*n+1), print1(n", ")))
%Y A301634 A163115 gives the primes.
%Y A301634 Numbers k such that b^k + b*k + 1 is prime: this sequence (b=2), A171058 (b=3), A301635 (b=5).
%Y A301634 Cf. A176691.
%K A301634 nonn,more,hard
%O A301634 1,3
%A A301634 _Seiichi Manyama_, Mar 25 2018
%E A301634 a(9)-a(15) from _Vaclav Kotesovec_, Mar 25 2018
%E A301634 a(16), a(18)-a(19) from _Jon E. Schoenfield_, Mar 26 2018
%E A301634 a(17) inserted by and a(20) from _Michael S. Branicky_, Jun 23 2024