A259772 -id:A259772 - cp's OEIS frontend

A304292 Primes p such that p + q^2 + r^3 is also prime, where p, q and r are consecutive primes.

31, 71, 79, 83, 89, 131, 137, 163, 179, 191, 251, 281, 331, 373, 401, 479, 569, 619, 659, 673, 701, 821, 881, 911, 929, 941, 947, 1093, 1291, 1301, 1373, 1409, 1459, 1481, 1559, 1583, 1657, 1811, 1907, 1973, 1987, 2003, 2089, 2243, 2309, 2339, 2341, 2357, 2423

Offset: 1

Paolo P. Lava, May 15 2018

Similar to A259772 where the condition is p and p^3 + q^2 + r both prime.

			a(1) = 31 is prime and 31 + 37^2 + 41^3 = 70321 is prime too.
a(2) = 71 is prime and 71 + 73^2 + 79^3 = 498439 is prime too.

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A259772.

select(n->isprime(n) and isprime(n+nextprime(n)^2+nextprime(nextprime(n))^3),[$1..2500]);

Select[Partition[Prime@ Range@ 400, 3, 1], PrimeQ[#1 + #2^2 + #3^3] & @@ # &][[All, 1]] (* Michael De Vlieger, May 27 2018 *)

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

Original entry on oeis.org

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

Offset: 1

Dumitru Damian, Oct 09 2021

nonn

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

			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.

Cf. A000040, A348313, A259772, A304292.

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

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()]

cp's OEIS Frontend

A304292 Primes p such that p + q^2 + r^3 is also prime, where p, q and r are consecutive primes.

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