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

1,1

Comments

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

Links

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

Example

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.

Maple

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

Mathematica

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

Crossrefs

Cf. A259772.

Sequence in context: A109309 A263242 A294625 * A127191 A003542 A055781

Adjacent sequences: A304289 A304290 A304291 * A304293 A304294 A304295

Keyword

nonn,easy

Author

Paolo P. Lava, May 15 2018

Status

approved