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

%I A241099 #9 Apr 19 2014 19:16:33
%S A241099 5,23,53,113,173,197,269,317,383,443,557,563,587,647,659,773,797,827,
%T A241099 947,983,1097,1103,1187,1217,1229,1889,1913,1949,2039,2099,2153,2213,
%U A241099 2339,2357,2399,2417,2447,2579,2693,2837,2879,2897,2903,2939,2969,3089,3203
%N A241099 Primes p such that (p^3 + 4)/3 is prime.
%H A241099 K. D. Bajpai, <a href="/A241099/b241099.txt">Table of n, a(n) for n = 1..8857</a>
%e A241099 5 is prime and appears in the sequence because (5^3 + 4)/3 = 43 which is a prime.
%e A241099 23 is prime and appears in the sequence because (23^3 + 4)/3 = 4057 which is a prime.
%p A241099 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);
%t A241099 Select[Prime[Range[500]], PrimeQ[(#^3 + 4)/3] &]
%t A241099 n = 0; Do[If[PrimeQ[(Prime[k]^3 + 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (* b-file *)
%Y A241099 Cf. A109953 (primes p:(p^2+1)/3 is prime).
%Y A241099 Cf. A118915 (primes p:(p^2+5)/6 is prime).
%Y A241099 Cf. A118918 (primes p:(p^2+11)/12 is prime).
%K A241099 nonn
%O A241099 1,1
%A A241099 _K. D. Bajpai_, Apr 15 2014