login
A301634
Numbers k such that 2^k + 2*k + 1 is prime.
3
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
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
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