

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, 37918, 40594
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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..18.


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: A149572 A149573 A149574 * 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) from Jon E. Schoenfield, Mar 26 2018


STATUS

approved



