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

1,1

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..15.

Example

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.

Mathematica

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

Prog

(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()]

Crossrefs

Cf. A000040, A348313, A259772, A304292.

Sequence in context: A017287 A017395 A017659 * A172767 A122557 A284101

Adjacent sequences: A348264 A348265 A348266 * A348268 A348269 A348270

Keyword

nonn

Author

Dumitru Damian, Oct 09 2021

Status

approved