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
Keywords
Examples
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.
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..1000
Programs
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Magma
[p: p in PrimesUpTo (3000) | IsPrime(k) where k is (p^3 + NextPrime(p)^2 + NextPrime(NextPrime(p)))];
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Maple
select(n -> isprime(n) and isprime((n)^3+nextprime(n)^2+nextprime(nextprime((n)))), [seq(n, n=1..10000)]);
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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 *)
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PARI
forprime(p=1, 3000, q=nextprime(p+1); r=nextprime(q+1); k=(p^3 + q^2 + r); if(isprime(k), print1(p,", ")))