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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A001912.

Sequence in context: A228456 A238717 A057013 * A249046 A237661 A116006

Adjacent sequences: A055752 A055753 A055754 * A055756 A055757 A055758

Keyword

easy,nonn

Author

Harvey P. Dale, Jul 12 2000

Extensions

More terms from James A. Sellers, Jul 13 2000

Status

approved