

A123924


Numbers k such that 2^(k+1) + 3^k is prime.


1



0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 15, 17, 22, 32, 33, 35, 36, 46, 47, 59, 63, 80, 101, 154, 159, 173, 221, 225, 236, 250, 281, 347, 789, 992, 1607, 1631, 1983, 2072, 3616, 3702, 5076, 5957, 6335
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OFFSET

1,3


COMMENTS

Also numbers n such that A123601(n) = A085279(n+1) = 2^(n+1) + 3^n. There are only 4 known primes of form the 2^k + 3^k, {2, 5, 13, 97} = A082101(n), corresponding to k = {0, 1, 2, 4}.


LINKS

Table of n, a(n) for n=1..43.


MATHEMATICA

Do[f=2^(n+1)+3^n; If[PrimeQ[f], Print[{n, f}]], {n, 0, 347}]
Select[Range[0, 6400], PrimeQ[2^(#+1)+3^#]&] (* Harvey P. Dale, Mar 04 2019 *)


PROG

(PARI) is(n)=ispseudoprime(2^(n+1)+3^n) \\ Charles R Greathouse IV, Jun 13 2017


CROSSREFS

Cf. A123601 = Smallest prime of the form p^n + q^n + r^n, where p, q, r are primes. Cf. A085279 = 2^n + 3^(n1). Cf. A082101 = Primes of form 2^k + 3^k.
Sequence in context: A116546 A108957 A080112 * A252484 A036023 A119952
Adjacent sequences: A123921 A123922 A123923 * A123925 A123926 A123927


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Nov 20 2006


EXTENSIONS

More terms from Stefan Steinerberger, May 12 2007


STATUS

approved



