A253772 Numbers k such that 4^k + 13 is prime.

1, 2, 4, 10, 19, 32, 40, 146, 566, 2054, 9967, 62639, 87814, 141092

Offset: 1

Author

Vincenzo Librandi, Jan 12 2015

Keywords

• nonn
• more

Comments

Numbers of the form 4^n+k (for n>0) are never primes when k is even (obviously) or when k == -1 (mod 6): in the last case, in fact, (3+1)^n + 6*h-1 is divisible by 3. - Bruno Berselli, Oct 06 2015

Crossrefs

Cf. A104067.

Cf. Numbers k such that 4^k + d is prime: A089437 (d=3), A217349 (d=7), A217350 (d=9), this sequence (d=13), A253773 (d=15), A253774 (d=19), A262345 (d=21), A204388 (d=25), A262969 (d=27), A262971 (d=31), A262972 (d=33).

Programs

Magma

[n: n in [0..2000] | IsPrime(4^n+13)];

Mathematica

Select[Range[4000], PrimeQ[4^# + 13] &]

PARI

is(n)=ispseudoprime(4^n+13) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = A102634(n)/2. - Elmo R. Oliveira, Nov 12 2023

Extensions

a(11)-a(14) derived from A102634 by Robert Price, Sep 06 2015