A348267 Primes of the form q^3+r^5+s^7, where q,r,s are consecutive primes.

19504103, 410711297, 895293793, 19205982415663, 27139128435043, 122997897555661, 2351321783571193, 33026024797765183, 44544286011297461, 257023170905666323, 630639912549644209, 896737512757442999, 2267254920439040789, 2344105012311523369, 25786002910400593997

Offset: 1

Author

Dumitru Damian, Oct 09 2021

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A000040, A348313, A259772, A304292.

Programs

Mathematica

Select[(#[[1]]^3 + #[[2]]^5 + #[[3]]^7) & /@ Partition[Select[Range[1000], PrimeQ], 3, 1], PrimeQ] (* Amiram Eldar, Oct 11 2021 *)

Sage

def Q3R5S7(x):
    return Primes().unrank(x)^3+Primes().unrank(x+1)^5+Primes().unrank(x+2)^7
A348267 = [Q3R5S7(x) for x in range(0,10^3) if Q3R5S7(x) in Primes()]