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

%I A304292 #15 May 29 2018 08:30:29
%S A304292 31,71,79,83,89,131,137,163,179,191,251,281,331,373,401,479,569,619,
%T A304292 659,673,701,821,881,911,929,941,947,1093,1291,1301,1373,1409,1459,
%U A304292 1481,1559,1583,1657,1811,1907,1973,1987,2003,2089,2243,2309,2339,2341,2357,2423
%N A304292 Primes p such that p + q^2 + r^3 is also prime, where p, q and r are consecutive primes.
%C A304292 Similar to A259772 where the condition is p and p^3 + q^2 + r both prime.
%H A304292 Seiichi Manyama, <a href="/A304292/b304292.txt">Table of n, a(n) for n = 1..1000</a>
%e A304292 a(1) = 31 is prime and 31 + 37^2 + 41^3 = 70321 is prime too.
%e A304292 a(2) = 71 is prime and 71 + 73^2 + 79^3 = 498439 is prime too.
%p A304292 select(n->isprime(n) and isprime(n+nextprime(n)^2+nextprime(nextprime(n))^3),[$1..2500]);
%t A304292 Select[Partition[Prime@ Range@ 400, 3, 1], PrimeQ[#1 + #2^2 + #3^3] & @@ # &][[All, 1]] (* _Michael De Vlieger_, May 27 2018 *)
%Y A304292 Cf. A259772.
%K A304292 nonn,easy
%O A304292 1,1
%A A304292 _Paolo P. Lava_, May 15 2018