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

%I A235705 #12 Apr 23 2014 16:05:35
%S A235705 19,59,269,349,409,419,479,769,929,1109,1319,1399,1979,2609,3659,4079,
%T A235705 4919,5309,5449,5879,6079,6299,6949,7069,7129,7229,7699,7829,8069,
%U A235705 8329,8599,9679,10729,11969,12809,13109,13229,13859,14159,14419,14629,14929,15259
%N A235705 Primes p such that (p^3 + 6)/5 is prime.
%C A235705 All the terms in the sequence are congruent to 1 or 3 mod 4.
%H A235705 K. D. Bajpai, <a href="/A235705/b235705.txt">Table of n, a(n) for n = 1..2640</a>
%e A235705 a(1) = 19 is prime: (19^3 + 6)/ 5 = 1373 which is also prime.
%e A235705 a(2) = 59 is prime: (59^3 + 6)/ 5 = 41077 which is also prime.
%p A235705 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);
%t A235705 Select[Prime[Range[5000]], PrimeQ[(#^3 + 6)/5] &]
%t A235705 n = 0; Do[If[PrimeQ[(Prime[k]^3 + 6)/5], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)
%o A235705 (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
%Y A235705 Cf. A109953 (primes p: (p^2+1)/3 is prime).
%Y A235705 Cf. A118915 (primes p: (p^2+5)/6 is prime).
%Y A235705 Cf. A118918 (primes p: (p^2+11)/12 is prime).
%Y A235705 Cf. A241101 (primes p: (p^3-4)/3 is prime).
%Y A235705 Cf. A241120 (primes p: (p^3+2)/3 is prime).
%K A235705 nonn
%O A235705 1,1
%A A235705 _K. D. Bajpai_, Apr 20 2014