A081507 Numbers k for which 2^k + 3^k + 4^k is prime.

0, 2, 4, 6, 8, 108, 144, 334, 1422, 4824, 16502, 19050, 23262

Offset

1,2

Comments

a(13) > 20838. - J.W.L. (Jan) Eerland, Dec 20 2021

Links

Table of n, a(n) for n=1..13.

Example

k=2: 2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29 (a prime).

Mathematica

Do[s=2^w+3^w+4^w; If[IntegerQ[w/100], Print[{w}]]; If[PrimeQ[s], Print[{w, s}]], {w, 0, 1000}]
Do[ If[ PrimeQ[2^w+3^w+4^w], Print[n]], {n, 0, 5000}]
Select[Range[5000], PrimeQ[Plus@@({2, 3, 4}^#)]&] (* Harvey P. Dale, Jan 03 2011 *)
DeleteCases[ParallelTable[If[PrimeQ[(2^n)+(3^n)+(4^n)], n, a], {n, 0, 19050}], a] (* J.W.L. (Jan) Eerland, Dec 20 2021 *)

Prog

(PARI) isok(k) = isprime(2^k + 3^k + 4^k); \\ Michel Marcus, Sep 05 2017
(Magma) [n: n in [0..400] | IsPrime(2^n+3^n+4^n)]; // Vincenzo Librandi, Sep 05 2017

Crossrefs

Cf. A081506.

Sequence in context: A083145 A085920 A228327 * A115336 A119666 A087302

Adjacent sequences: A081504 A081505 A081506 * A081508 A081509 A081510

Keyword

nonn,more

Author

Labos Elemer, Apr 15 2003

Extensions

a(9)-a(10) from Robert G. Wilson v, Jul 22 2005

a(11)-a(12) from J.W.L. (Jan) Eerland, Dec 20 2021

Offset corrected by Jon E. Schoenfield, Dec 20 2021

a(13) from Michael S. Branicky, Mar 31 2023

Status

approved