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%I #43 Mar 28 2018 04:52:40
%S 0,1,5,13,65,85,229,2005,3875,3919,5417,8819,11899,16668,19445,28242,
%T 37918,40594
%N Numbers k such that 2^k + 2*k + 1 is prime.
%C 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 a:=k->`if`(isprime(2^k+2*k+1),k,NULL): seq(a(k),k=0..6000); # _Muniru A Asiru_, Mar 25 2018
%t Flatten[{0, Select[Range[5000], PrimeQ[2^# + 2*# + 1] &]}] (* _Vaclav Kotesovec_, Mar 25 2018 *)
%o (PARI) for(n=0, 500, if(isprime(2^n+2*n+1), print1(n", ")))
%Y A163115 gives the primes.
%Y Numbers k such that b^k + b*k + 1 is prime: this sequence (b=2), A171058 (b=3), A301635 (b=5).
%Y Cf. A176691.
%K nonn,more,hard
%O 1,3
%A _Seiichi Manyama_, Mar 25 2018
%E a(9)-a(15) from _Vaclav Kotesovec_, Mar 25 2018
%E a(16)-a(18) from _Jon E. Schoenfield_, Mar 26 2018
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