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

1,1

Links

Table of n, a(n) for n=1..52.

Example

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

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 *)

Prog

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

Crossrefs

Subsequence of A253142, A086303 and A121982.

Sequence in context: A076434 A192150 A049441 * A193868 A256788 A324211

Adjacent sequences: A253140 A253141 A253142 * A253144 A253145 A253146

Keyword

nonn

Author

Zak Seidov, Dec 27 2014

Status

approved