A235705 Primes p such that (p^3 + 6)/5 is prime.

19, 59, 269, 349, 409, 419, 479, 769, 929, 1109, 1319, 1399, 1979, 2609, 3659, 4079, 4919, 5309, 5449, 5879, 6079, 6299, 6949, 7069, 7129, 7229, 7699, 7829, 8069, 8329, 8599, 9679, 10729, 11969, 12809, 13109, 13229, 13859, 14159, 14419, 14629, 14929, 15259

Offset: 1

Author

K. D. Bajpai, Apr 20 2014

Keywords

• nonn

Comments

All the terms in the sequence are congruent to 1 or 3 mod 4.

Examples

			a(1) = 19 is prime: (19^3 + 6)/ 5 = 1373 which is also prime.
a(2) = 59 is prime: (59^3 + 6)/ 5 = 41077 which is also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2640

Crossrefs

Cf. A109953 (primes p: (p^2+1)/3 is prime).

Cf. A118915 (primes p: (p^2+5)/6 is prime).

Cf. A118918 (primes p: (p^2+11)/12 is prime).

Cf. A241101 (primes p: (p^3-4)/3 is prime).

Cf. A241120 (primes p: (p^3+2)/3 is prime).

Programs

Maple

KD:= proc() local a,b; a:=ithprime(n); b:=(a^3+6)/5; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..5000);

Mathematica

Select[Prime[Range[5000]], PrimeQ[(#^3 + 6)/5] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 6)/5], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)

PARI

s=[]; forprime(p=2, 20000, if((p^3+6)%5==0 && isprime((p^3+6)/5), s=concat(s, p))); s \\ Colin Barker, Apr 21 2014