A291464 Primes p such that p^3*q^3 + p^2 + q^2 is prime, where q is next prime after p.

2, 11, 13, 41, 97, 277, 389, 1093, 1229, 1409, 1429, 1627, 1823, 1931, 1979, 2437, 2521, 2549, 2657, 2689, 2719, 2729, 2731, 2969, 3019, 3413, 3539, 3593, 3613, 3623, 3697, 4003, 4027, 4289, 4327, 4583, 4751, 5051, 5323, 5503, 5657, 5783, 6143, 6221, 6299, 6329

Offset

1,1

Links

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

Example

a(1) = 2 is prime; 3 is the next prime: 2^3*3^3 + 2^2 + 3^2 = 8*27 + 4 + 9 = 229 that is a prime.
a(2) = 11 is prime; 13 is the next prime: 11^3*13^3 + 11^2 + 13^2 = 1331*2197 + 121 + 169 = 2924497 that is a prime.

Maple

select(p -> andmap(isprime, [p, (p^3*nextprime(p)^3+p^2+nextprime(p)^2)]), [seq(p, p=1..10^4)]);

Mathematica

Select[Prime[Range[5000]], PrimeQ[#^3*NextPrime[#]^3 + #^2 + NextPrime[#]^2] &]
Select[Partition[Prime[Range[1000]], 2, 1], PrimeQ[#[[1]]^3 #[[2]]^3+#[[1]]^2+#[[2]]^2]&][[;; , 1]] (* Harvey P. Dale, Sep 11 2023 *)

Prog

(PARI) forprime(p=1, 5000, q=nextprime(p+1); p3=p^3; p2=p^2; q3=q^3; q2=q^2; if(ispseudoprime(p3*q3 + p2 + q2), print1(p, ", ")));
(Magma) [p: p in PrimesUpTo(5000) | IsPrime(p^3*q^3 + p^2 + q^2) where q is NextPrime(p)];

Crossrefs

Cf. A000040, A001043, A006094, A030078, A096342, A120398, A126148, A152241, A291339, A291374.

Sequence in context: A106960 A084405 A041447 * A262832 A091021 A042563

Adjacent sequences: A291461 A291462 A291463 * A291465 A291466 A291467

Keyword

nonn

Author

K. D. Bajpai, Aug 24 2017

Status

approved