A128780 Numbers n such that n^k+(n+1)^k is prime for k = 1, 2, 4.

1, 2, 9, 14, 189, 204, 230, 320, 680, 765, 1080, 1190, 1359, 1364, 1500, 1764, 1850, 2049, 2115, 2360, 2379, 2919, 3050, 3110, 3179, 3579, 3794, 4164, 4215, 4470, 5355, 5619, 5630, 5664, 5810, 5889, 5979, 6035, 6150, 6269, 6824, 6960, 7275, 8045, 8259

Offset: 1

Author

Zak Seidov, Mar 28 2007

Keywords

• nonn

Comments

n^k+(n+1)^k is prime only for k = power of 2.

There are 1242 terms < 10^6.

All terms > 2 are congruent to 0 or 4 (mod 5). - Robert Israel, Mar 29 2017

Examples

			{2+1, 2^2+3^2,2^4+3^4} = {3,13,97} all prime,
{9+10, 9^2+10^2,9^4+10^4} = {19,181,16561} all prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subset of A068501.

Programs

Maple

select(n -> isprime(2*n+1) and isprime(2*n^2+2*n+1) and isprime(n^4+(n+1)^4),
[1,2,seq(seq(5*i+j,j=[0,4]),i=1..10000)]); # Robert Israel, Mar 29 2017

Mathematica

pnQ[n_]:=And@@PrimeQ/@(n^{1,2,4}+(n+1)^{1,2,4}); Select[Range[9000], pnQ]  (* Harvey P. Dale, Apr 06 2011 *)