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

1,2

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

Links

Table of n, a(n) for n=1..14.

Formula

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

Mathematica

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

Prog

(Magma) [n: n in [0..2000] | IsPrime(4^n+13)];
(PARI) is(n)=ispseudoprime(4^n+13) \\ Charles R Greathouse IV, Feb 17 2017

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).

Sequence in context: A257593 A197926 A228705 * A043330 A295961 A219555

Adjacent sequences: A253769 A253770 A253771 * A253773 A253774 A253775

Keyword

nonn,more

Author

Vincenzo Librandi, Jan 12 2015

Extensions

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

Status

approved