

A259772


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


2



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

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


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[#]]]&]


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

Cf. A000040, A034962, A133529, A133530, A258269, A304292.
Sequence in context: A029473 A103088 A226925 * A082387 A032923 A018750
Adjacent sequences: A259769 A259770 A259771 * A259773 A259774 A259775


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Jul 05 2015


STATUS

approved



