A055755 4n^2+1, 2n^2+1, 2n^2-1 are all prime.

3, 42, 45, 102, 132, 153, 237, 297, 375, 468, 570, 990, 2085, 2478, 2712, 3240, 4743, 5382, 5517, 6828, 7962, 8970, 8982, 9033, 9570, 9612, 9747, 9813, 10692, 12363, 12453, 12468, 12750, 13902, 14763, 14925, 15750, 16365, 17118, 17688, 19527

Offset: 1

Author

Harvey P. Dale, Jul 12 2000

Keywords

• easy
• nonn

Examples

			42 is included because 4*42^2+1, 2*42^2+1, 2*42^2-1 are all prime numbers.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001912.

Programs

Maple

with(numtheory): for n from 1 to 50000 do if isprime(4*n^2+1) and isprime(2*n^2+1) and isprime(2*n^2-1) then printf(`%d,`,n) fi: od:

Mathematica

a={};Do[If[PrimeQ[4n^2+1] && PrimeQ[2n^2+1] && PrimeQ[2n^2-1], AppendTo[a,n]], {n,10000}]; a (* Peter J. C. Moses, Apr 02 2013 *)

Extensions

More terms from James Sellers, Jul 13 2000