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

1,3

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

Links

Table of n, a(n) for n=1..20.

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 *)

Prog

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

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.

Sequence in context: A149573 A149574 A372383 * A309167 A272069 A018678

Adjacent sequences: A301631 A301632 A301633 * A301635 A301636 A301637

Keyword

nonn,more,hard

Author

Seiichi Manyama, Mar 25 2018

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

Status

approved