A348313 Primes q such that q^3+r^5+s^7 is also prime, where q,r,s are consecutive primes.

5, 11, 13, 71, 73, 97, 149, 223, 229, 283, 337, 353, 401, 409, 577, 827, 887, 1051, 1277, 1321, 1489, 1543, 1627, 1787, 1931, 2237, 2467, 2903, 3137, 3181, 3559, 3917, 4243, 4357, 4363, 4441, 4583, 4723, 4933, 5113, 5693, 5839, 5857, 6007, 6043, 6053, 6121

Offset: 1

Author

Dumitru Damian, Oct 11 2021

Keywords

• nonn

Comments

Exponent values (3,5,7) given by the prime triplet of the form p, p+2, p+4.

Examples

			5 is a term because 5^3+7^5+11^7 = 19504103 is prime;
11 is a term because 11^3+13^5+17^7 = 410711297 is prime.
		

Crossrefs

Cf. A000040, A348267.

Programs

Mathematica

Select[Partition[Select[Range[6000], PrimeQ], 3, 1], PrimeQ[#[[1]]^3 + #[[2]]^5 + #[[3]]^7] &][[;; , 1]] (* Amiram Eldar, Oct 11 2021 *)

PARI

isok(p) = if (isprime(p), my(q=nextprime(p+1), r=nextprime(q+1)); isprime(p^3+q^5+r^7)); \\ Michel Marcus, Oct 11 2021

Sage

def Q(x):
    if Primes().unrank(x)^3+Primes().unrank(x+1)^5+Primes().unrank(x+2)^7 in Primes():
       return Primes().unrank(x)
A348313 = [Q(x) for x in range(0,10^3) if Q(x)!=None]