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A259772 Primes p such that p^3 + q^2 + r is also prime, where p,q,r are consecutive primes. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
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.
MAPLE
select(n -> isprime(n) and isprime((n)^3+nextprime(n)^2+nextprime(nextprime((n)))), [seq(n, n=1..10000)]);
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 *)
PROG
(PARI) forprime(p=1, 3000, q=nextprime(p+1); r=nextprime(q+1); k=(p^3 + q^2 + r); if(isprime(k), print1(p, ", ")))
(Magma) [p: p in PrimesUpTo (3000) | IsPrime(k) where k is (p^3 + NextPrime(p)^2 + NextPrime(NextPrime(p)))];
CROSSREFS
Sequence in context: A029473 A103088 A226925 * A082387 A032923 A018750
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jul 05 2015
STATUS
approved

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Last modified May 21 19:35 EDT 2024. Contains 372738 sequences. (Running on oeis4.)