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

%I A259772 #18 Sep 08 2022 08:46:13
%S A259772 3,17,19,43,53,89,107,149,293,401,439,449,659,809,821,937,1009,1031,
%T A259772 1091,1097,1123,1163,1181,1259,1277,1367,1427,1657,1721,1777,1789,
%U A259772 1811,1987,2027,2063,2207,2333,2417,2503,2657,2713,3067,3079,3083,3251,3389,3491,3527
%N A259772 Primes p such that p^3 + q^2 + r is also prime, where p,q,r are consecutive primes.
%H A259772 Seiichi Manyama, <a href="/A259772/b259772.txt">Table of n, a(n) for n = 1..1000</a>
%e A259772 a(2) = 17 is prime: 17^3 + 19^2 + 23 = 5297 which is also prime.
%e A259772 a(3) = 19 is prime: 19^3 + 23^2 + 29 = 7417 which is also prime.
%p A259772 select(n -> isprime(n) and isprime((n)^3+nextprime(n)^2+nextprime(nextprime((n)))), [seq(n, n=1..10000)]);
%t A259772 Select[Prime[Range[1000]], PrimeQ[#^3 + NextPrime[#]^2 + NextPrime[NextPrime[#]]]&]
%t A259772 Select[Partition[Prime[Range[500]],3,1],PrimeQ[#[[1]]^3+ #[[2]]^2+ #[[3]]]&][[All,1]] (* _Harvey P. Dale_, Dec 23 2021 *)
%o A259772 (PARI) forprime(p=1, 3000, q=nextprime(p+1); r=nextprime(q+1); k=(p^3 + q^2 + r); if(isprime(k), print1(p,", ")))
%o A259772 (Magma) [p: p in PrimesUpTo (3000) | IsPrime(k) where k is (p^3 + NextPrime(p)^2 + NextPrime(NextPrime(p)))];
%Y A259772 Cf. A000040, A034962, A133529, A133530, A258269, A304292.
%K A259772 nonn
%O A259772 1,1
%A A259772 _K. D. Bajpai_, Jul 05 2015