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A163425 Primes p such that (p-1)^3/8+(p+1)^2/4 is also prime.

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%I A163425 #9 Sep 08 2022 08:45:46
%S A163425 3,5,7,17,19,29,31,47,61,71,79,101,131,167,181,197,199,227,251,269,
%T A163425 281,307,359,397,421,449,461,467,509,569,659,691,709,811,859,919,937,
%U A163425 997,1031,1087,1151,1217,1231,1249,1277,1279,1301,1307,1361,1409,1447,1451
%N A163425 Primes p such that (p-1)^3/8+(p+1)^2/4 is also prime.
%C A163425 The associated (p-1)^3/8+(p+1)^2/4 are in A163424.
%H A163425 Vincenzo Librandi, <a href="/A163425/b163425.txt">Table of n, a(n) for n = 1..1000</a>
%e A163425 p=3 is in the sequence because (3-1)^3/8+(3+1)^2/4=1+4=5 is also prime.
%e A163425 p=5 is in the sequence because (5-1)^3/8+(5+1)^2/4=17 is also prime.
%t A163425 f[n_]:=((p-1)/2)^3+((p+1)/2)^2; lst={};Do[p=Prime[n];If[PrimeQ[f[p]], AppendTo[lst,p]],{n,7!}];lst
%t A163425 Select[Prime[Range[1500]], PrimeQ[(# - 1)^3 / 8 + (# + 1)^2 / 4]&] (* _Vincenzo Librandi_, Apr 08 2013 *)
%o A163425 (Magma) [p: p in PrimesInInterval(3, 2000) | IsPrime((p-1)^3 div 8 + (p+1)^2 div 4)]; // _Vincenzo Librandi_, Apr 08 2013
%Y A163425 Cf. A162652, A163418, A163419, A163420, A163421, A163422.
%K A163425 nonn,easy
%O A163425 1,1
%A A163425 _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009
%E A163425 Comment turned into examples by _R. J. Mathar_, Sep 02 2009