A304292 -id:A304292 - cp's OEIS frontend

A259772 Primes p such that p^3 + q^2 + r is also prime, where p,q,r are consecutive primes.

3, 17, 19, 43, 53, 89, 107, 149, 293, 401, 439, 449, 659, 809, 821, 937, 1009, 1031, 1091, 1097, 1123, 1163, 1181, 1259, 1277, 1367, 1427, 1657, 1721, 1777, 1789, 1811, 1987, 2027, 2063, 2207, 2333, 2417, 2503, 2657, 2713, 3067, 3079, 3083, 3251, 3389, 3491, 3527

Offset: 1

K. D. Bajpai, Jul 05 2015

nonn

			a(2) = 17 is prime: 17^3 + 19^2 + 23 = 5297 which is also prime.
a(3) = 19 is prime: 19^3 + 23^2 + 29 = 7417 which is also prime.

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

Cf. A000040, A034962, A133529, A133530, A258269, A304292.

[p: p in PrimesUpTo (3000) | IsPrime(k) where k is (p^3 + NextPrime(p)^2 + NextPrime(NextPrime(p)))];

select(n -> isprime(n) and isprime((n)^3+nextprime(n)^2+nextprime(nextprime((n)))), [seq(n, n=1..10000)]);

Select[Prime[Range[1000]], PrimeQ[#^3 + NextPrime[#]^2 + NextPrime[NextPrime[#]]]&]
Select[Partition[Prime[Range[500]],3,1],PrimeQ[#[[1]]^3+ #[[2]]^2+ #[[3]]]&][[All,1]] (* Harvey P. Dale, Dec 23 2021 *)

forprime(p=1, 3000, q=nextprime(p+1); r=nextprime(q+1); k=(p^3 + q^2 + r); if(isprime(k), print1(p,", ")))

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

A259772 Primes p such that p^3 + q^2 + r is also prime, where p,q,r are consecutive primes.

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