A253143 Numbers n such that n + 15, n^2 + 15 and n^3 + 15 are prime.

2, 4, 16, 22, 32, 44, 86, 88, 98, 298, 316, 452, 602, 638, 658, 736, 862, 868, 896, 1276, 1358, 1586, 1768, 1996, 2342, 2366, 2444, 2452, 2542, 2788, 2902, 3242, 3448, 3704, 3718, 3998, 4376, 4552, 4928, 5422, 5504, 5566, 5608, 5644, 5728, 5768, 5776, 6664, 6934, 6946, 7708, 7858

Offset: 1

Author

Zak Seidov, Dec 27 2014

Keywords

• nonn

Examples

			With n=2, n+15 (17), n^2+15 (19) and n^3+15 (23) are all prime.
		

Crossrefs

Subsequence of A253142, A086303 and A121982.

Programs

Mathematica

p = 15; Select[Range[2, 20000, 2], PrimeQ[p + #^3] && PrimeQ[p + #^2] && PrimeQ[p + #] &]
Select[Range[2,8000,2],AllTrue[#^Range[3]+15,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 29 2018 *)

PARI

isok(n) = isprime(n+15) && isprime(n^2 + 15) && isprime(n^3 + 15); \\ Michel Marcus, Dec 28 2014