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%I #14 Sep 08 2022 08:45:46
%S 3,5,7,11,13,17,19,31,37,43,59,61,79,83,89,97,107,109,113,139,149,167,
%T 191,233,241,263,271,293,307,311,337,359,373,383,439,443,479,487,491,
%U 523,557,617,641,647,659,673,683,701,733,757,811,829,853,857,859,877
%N Primes p such that A071568((p-1)/2) is also prime.
%C Primes p such that (p-1)^3/8+(p+1)/2 is also prime, i.e., in A095692.
%H Vincenzo Librandi, <a href="/A163422/b163422.txt">Table of n, a(n) for n = 1..1000</a>
%e p=3 is in the sequence because (3-1)^3/8+(3+1)/2=3 is prime.
%e p=5 is in the sequence because (5-1)^3/8+(5+1)/2=11 is prime.
%t f[n_]:=((n-1)/2)^3+((n+1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n,6!}]; lst
%t Select[Prime[Range[180]], PrimeQ[(#-1)^3/8+(#+1)/2]&] (* _Harvey P. Dale_, Jan 05 2011 *)
%o (Magma) [p: p in PrimesUpTo(1000) | IsPrime((p^3-3*p^2+7*p+3) div 8)]; // _Vincenzo Librandi_, Apr 10 2013
%Y Cf. A162652, A163418, A163419, A163420, A163421.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009
%E Definition rewritten by _R. J. Mathar_, Aug 17 2009