A127206 Numbers k such that k^j + (k+1)^j is prime for j = 1, 2, 4, 8.

1, 765, 39269, 70260, 71399, 85764, 100079, 167789, 218229, 307020, 388449, 468945, 514760, 553400, 568904, 782595, 826284, 1160199, 1220430, 1403775, 1633020, 1714739, 1727930, 1788144, 1932900, 1958705, 2023119, 2037450, 2178804, 2185520, 2193969, 2238474, 2264774

Offset: 1

Author

Zak Seidov, Mar 28 2007

Keywords

• nonn

Comments

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

Subset of A128780 which is a subset of A068501.

Examples

			{765 + 766, 765^2 + 766^2, 765^4 + 766^4, 765^8 + 766^8} = {1531, 1171981, 686770904161, 235828747162526935093921}, all prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..331

Crossrefs

Cf. A068501, A128780.

Programs

Magma

[n: n in [1..3*10^6]| IsPrime(2*n+1) and IsPrime(n^2+(n+1)^2) and IsPrime(n^4+(n+1)^4) and IsPrime(n^8+(n+1)^8)]; // Vincenzo Librandi, Nov 18 2018

Mathematica

Do[If[PrimeQ[2n + 1] && PrimeQ[n^2 + (n+1)^2] && PrimeQ[n^4 + (n+1)^4] && PrimeQ[n^8 + (n+1)^8], Print[n]], {n, 5*10^6}] (* Ryan Propper, Mar 30 2007 *)

Extensions

More terms from Ryan Propper, Mar 30 2007