A291339 Primes p such that p^3*q^3 + p^3 + q^3 is prime, where q is the next prime after p.

2, 3, 7, 19, 37, 47, 83, 89, 107, 137, 181, 251, 257, 349, 379, 569, 631, 653, 677, 691, 797, 823, 839, 863, 883, 919, 1009, 1021, 1223, 1229, 1361, 1423, 1571, 1609, 1831, 1873, 1907, 1993, 2053, 2113, 2207, 2239, 2293, 2309, 2579, 2833, 3137, 3319, 3593, 3673

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(2) = 3 is prime; 5 is the next prime: 3^3*5^3 + 3^3 + 5^3 = 27*125 + 27 + 125 = 3527 that is a prime.
a(3) = 7 is prime; 11 is the next prime: 7^3*11^3 + 7^3 + 11^3 = 343*1331 + 343 + 1331 = 458207 that is a prime.

Maple

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

Mathematica

Prime@Select[Range[1000], PrimeQ[Prime[#]^3*Prime[# + 1]^3 + Prime[#]^3 + Prime[# + 1]^3] &]

Prog

(Magma) [p: p in PrimesUpTo (5000) | IsPrime(p^3*q^3+p^3+q^3)];
(PARI) is(n) = my(q=nextprime(n+1)); ispseudoprime(n^3*q^3+n^3+q^3)
forprime(p=1, 3700, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Aug 22 2017
(PARI) list(lim)=my(v=List(), p=2, p3=8, q3); forprime(q=3, nextprime(lim\1+1), q3=q^3; if(isprime(p3*q3+p3+q3), listput(v, p)); p=q; p3=q3); Vec(v) \\ Charles R Greathouse IV, Aug 23 2017

Crossrefs

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

Sequence in context: A340281 A172461 A253971 * A235616 A257551 A091410

Adjacent sequences: A291336 A291337 A291338 * A291340 A291341 A291342

Keyword

nonn

Author

K. D. Bajpai, Aug 22 2017

Status

approved