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

Author

Paolo P. Lava, May 15 2018

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A259772.

Programs

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 *)