A339917 Primes p such that p+k and p^2+k are prime, where k = (p^2-1)/6.

13, 19, 71, 89, 103, 139, 233, 269, 409, 733, 1009, 1201, 1453, 1579, 1601, 1723, 2053, 2143, 2251, 2699, 2753, 3181, 3259, 3271, 3361, 3491, 3739, 3923, 4051, 4159, 4231, 4283, 4483, 4639, 4733, 5059, 5413, 5431, 5449, 6481, 6911, 7069, 7109, 7253, 7523, 7541, 7703, 7723, 7789, 7901, 8209, 9433

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 22 2020

Keywords

• nonn

Examples

			a(3) = 71 is a term because with k = (71^2-1)/6 = 840, 71, 71+840 = 911 and 71^2+840 = 5881 are all primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A084922, A339527.

Programs

Maple

select(p -> isprime(p) and isprime((7*p^2-1)/6) and isprime((p^2+6*p-1)/6), [seq(seq(6*i+j,j=[1,5]),i=0..10000)]);

PARI

isok(p) = isprime(p) && iferr(isprime(p+(p^2-1)/6) && isprime(p^2+(p^2-1)/6), E,0); \\ Michel Marcus, Dec 23 2020