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A291464 Primes p such that p^3*q^3 + p^2 + q^2 is prime, where q is next prime after p. 1
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 (list; graph; refs; listen; history; text; internal format)
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] &]

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

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Last modified October 27 10:47 EDT 2021. Contains 348274 sequences. (Running on oeis4.)