A081505 Primes of form 4^k + 3^k.

2, 7, 337, 4338014017

Offset

1,1

Comments

a(5) > 10^10000, so the next term (if it exists) is too large to include.

Links

Table of n, a(n) for n=1..4.

William A. Bogley and Gerald Williams, Efficient finite groups arising in the study of relative asphericity, Math. Z. 284, No. 1-2, 507-535 (2016).

Example

m=4: 4^4+3^4=256+81=337 prime.
Exponents for first 4 terms are {0,1,4,16}.

Mathematica

Do[s=3^w+4^w; If[IntegerQ[w/100], Print[{w}]]; If[PrimeQ[s], Print[{w, s}]], {w, 0, 3400}]
Do[ If[ PrimeQ[3^n+4^n], Print[3^n+4^n]], {n, 0, 10000}]
Select[Table[4^n+3^n, {n, 0, 20}], PrimeQ] (* Harvey P. Dale, Mar 07 2017 *)

Crossrefs

Cf. A059801, A074605.

Sequence in context: A048122 A144787 A118910 * A176748 A262088 A110386

Adjacent sequences: A081502 A081503 A081504 * A081506 A081507 A081508

Keyword

nonn

Author

Labos Elemer, Apr 15 2003

Status

approved