A301634 Numbers k such that 2^k + 2*k + 1 is prime.

0, 1, 5, 13, 65, 85, 229, 2005, 3875, 3919, 5417, 8819, 11899, 16668, 19445, 28242, 33407, 37918, 40594, 141251

Offset: 1

Author

Seiichi Manyama, Mar 25 2018

Keywords

• nonn
• more
• hard

Comments

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

Crossrefs

A163115 gives the primes.

Numbers k such that b^k + b*k + 1 is prime: this sequence (b=2), A171058 (b=3), A301635 (b=5).

Cf. A176691.

Programs

Maple

a:=k->`if`(isprime(2^k+2*k+1),k,NULL): seq(a(k),k=0..6000); # Muniru A Asiru, Mar 25 2018

Mathematica

Flatten[{0, Select[Range[5000], PrimeQ[2^# + 2*# + 1] &]}] (* Vaclav Kotesovec, Mar 25 2018 *)

PARI

for(n=0, 500, if(isprime(2^n+2*n+1), print1(n", ")))

Extensions

a(9)-a(15) from Vaclav Kotesovec, Mar 25 2018

a(16), a(18)-a(19) from Jon E. Schoenfield, Mar 26 2018

a(17) inserted by and a(20) from Michael S. Branicky, Jun 23 2024