A081506 Primes of the form 2^k + 3^k + 4^k.

3, 29, 353, 4889, 72353, 105312291668560568089831550410013687058921146068446092937783402353

Offset: 1

Author

Labos Elemer, Apr 15 2003

Keywords

• nonn

Comments

The next term (a(7)) has 202 digits. - Harvey P. Dale, Aug 20 2015

Examples

			k = 2: 2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29, which is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A074526, A081507.

Programs

Mathematica

Do[s=2^w+3^w+4^w; If[IntegerQ[w/100], Print[{w}]]; If[PrimeQ[s], Print[{w, s}]], {w, 0, 1000}]
Select[Table[2^n+3^n+4^n,{n,0,200}],PrimeQ] (* Harvey P. Dale, Aug 20 2015 *)

PARI

lista(kmax) = {my(p); for(k = 0, kmax, p = 2^k + 3^k + 4^k; if(isprime(p), print1(p, ", ")));} \\ Amiram Eldar, Aug 17 2024

Formula

a(n) = A074526(A081507(n)). - Amiram Eldar, Aug 17 2024