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Primes of the form (1+p+p^3)/3, p are prime numbers.
1

%I #4 Apr 09 2016 07:43:46

%S 2293,9941,895253,2626933,17298497,33084437,47685397,62056661,

%T 76782337,144599617,189907873,211280213,258717493,301410677,479690273,

%U 630940097,717228821,778918037,1035249013,1814163413,1889439157,2710909781

%N Primes of the form (1+p+p^3)/3, p are prime numbers.

%C 2293=(1+19+19^3)/3,..

%H Harvey P. Dale, <a href="/A163513/b163513.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_]:=(1+n+n^3)/3; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,7!}];lst

%t Select[(1+#+#^3)/3&/@Prime[Range[400]],PrimeQ] (* _Harvey P. Dale_, Apr 09 2016 *)

%Y Cf. A163512

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 29 2009