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

1,1

Comments

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

Links

Table of n, a(n) for n=1..47.

Example

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.

Mathematica

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

Prog

(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]
(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

Crossrefs

Cf. A000040, A348267.

Sequence in context: A018607 A032481 A365502 * A352534 A236411 A073615

Adjacent sequences: A348310 A348311 A348312 * A348314 A348315 A348316

Keyword

nonn

Author

Dumitru Damian, Oct 11 2021

Status

approved