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

1,1

Links

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

Example

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.

Maple

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

Mathematica

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 *)

Prog

(PARI) forprime(p=1, 3000, q=nextprime(p+1); r=nextprime(q+1); k=(p^3 + q^2 + r); if(isprime(k), print1(p, ", ")))
(Magma) [p: p in PrimesUpTo (3000) | IsPrime(k) where k is (p^3 + NextPrime(p)^2 + NextPrime(NextPrime(p)))];

Crossrefs

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

Sequence in context: A029473 A103088 A226925 * A082387 A032923 A018750

Adjacent sequences: A259769 A259770 A259771 * A259773 A259774 A259775

Keyword

nonn

Author

K. D. Bajpai, Jul 05 2015

Status

approved