A241099 Primes p such that (p^3 + 4)/3 is prime.

5, 23, 53, 113, 173, 197, 269, 317, 383, 443, 557, 563, 587, 647, 659, 773, 797, 827, 947, 983, 1097, 1103, 1187, 1217, 1229, 1889, 1913, 1949, 2039, 2099, 2153, 2213, 2339, 2357, 2399, 2417, 2447, 2579, 2693, 2837, 2879, 2897, 2903, 2939, 2969, 3089, 3203

Offset: 1

Author

K. D. Bajpai, Apr 15 2014

Keywords

• nonn

Examples

			5 is prime and appears in the sequence because (5^3 + 4)/3 = 43 which is a prime.
23 is prime and appears in the sequence because (23^3 + 4)/3 = 4057 which is a prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..8857

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).

Programs

Maple

KD:= proc() local a,b;a:=ithprime(n); b:=(a^3+4)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);

Mathematica

Select[Prime[Range[500]], PrimeQ[(#^3 + 4)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (* b-file *)