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%I #8 Apr 19 2014 19:16:58
%S 13,19,31,193,211,223,229,271,331,571,619,691,739,751,853,991,1009,
%T 1039,1051,1231,1303,1321,1549,1741,1789,1831,1993,1999,2029,2089,
%U 2113,2143,2203,2311,2521,2551,2683,2749,2851,3121,3259,3331,3571,3631,3823,3853,4093
%N Primes p such that (p^3 + 2)/3 is prime.
%H K. D. Bajpai, <a href="/A241120/b241120.txt">Table of n, a(n) for n = 1..8879</a>
%e 13 is prime and appears in the sequence because (13^3 + 2)/3 = 733 which is a prime.
%e 31 is prime and appears in the sequence because (31^3 + 2)/3 = 9931 which is a prime.
%p KD:= proc() local a,b;a:=ithprime(n); b:=(a^3+2)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);
%t Select[Prime[Range[500]], PrimeQ[(#^3 + 2)/3] &]
%t n = 0; Do[If[PrimeQ[(Prime[k]^3 + 2)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (* b-file *)
%o (PARI) s=[]; forprime(p=2, 8000, if((p^3+2)%3==0 && isprime((p^3+2)/3), s=concat(s, p))); s \\ _Colin Barker_, Apr 16 2014
%Y Cf. A109953 (primes p: (p^2+1)/3 is prime).
%Y Cf. A118915 (primes p: (p^2+5)/6 is prime).
%Y Cf. A118918 (primes p: (p^2+11)/12 is prime).
%Y Cf. A241101 (primes p: (p^3-4)/3 is prime).
%K nonn
%O 1,1
%A _K. D. Bajpai_, Apr 16 2014
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