A215248 Numbers n such that n^2 + 1 and (n^2+2)/6 are both primes.

4, 10, 16, 20, 26, 56, 110, 116, 170, 224, 236, 314, 326, 340, 430, 584, 700, 764, 920, 946, 1054, 1106, 1276, 1294, 1406, 1546, 1550, 1654, 1684, 1700, 1756, 1766, 1784, 1816, 2006, 2026, 2116, 2260, 2294, 2314, 2320, 2360, 2576, 2600, 2684, 2746, 2770, 2924

Offset

1,1

Comments

n==2 or 4 (mod 6) so that (n^2+2)/6 is an integer. - Robert Israel, May 03 2017

Links

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

Example

4 is in the sequence because 4^2+1 = 17 and (4^2+2)/6 = 3 are both primes.

Maple

select(t -> isprime(t^2+1) and isprime((t^2+2)/6), [seq(seq(6*j+k, k=[2, 4]), j=0..1000)]); # Robert Israel, May 03 2017

Mathematica

Select[Range[3000], PrimeQ[(#^2+1)]&&PrimeQ[(#^2+2)/6]&]
Select[Range[3000], AllTrue[{#^2+1, (#^2+2)/6}, PrimeQ]&] (* Harvey P. Dale, Sep 08 2024 *)

Crossrefs

Cf. A005574, A002496.

Sequence in context: A310503 A310504 A310505 * A310506 A310507 A334115

Adjacent sequences: A215245 A215246 A215247 * A215249 A215250 A215251

Keyword

nonn

Author

Michel Lagneau, Aug 10 2012

Status

approved