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%I #12 Sep 08 2022 08:45:46
%S 5,7,13,19,29,31,41,53,71,101,103,109,173,191,199,223,229,233,239,257,
%T 269,277,331,383,397,431,491,569,571,599,619,631,719,733,751,757,761,
%U 823,857,859,863,887,907,937,967,971,977,1009,1019,1063,1069,1123,1163
%N Primes p such that (p+1)^3/8+(p-1)/2 is also prime.
%C Primes A000040(k) such that (A006254(k-1))^3+ A005097(k-1) is also prime.
%H Vincenzo Librandi, <a href="/A163427/b163427.txt">Table of n, a(n) for n = 1..1000</a>
%F (a(n)+1)^3/8+(a(n)-1)/2 = A163426(n).
%e For p=5, (5+1)^3/8+(5-1)/2=27+2=29, prime, which adds p=5 to the sequence.
%e For p=7, (7+1)^3/8+(7-1)/2=67, prime, which adds p=7 to the sequence.
%t f[n_]:=((p+1)/2)^3+((p-1)/2); lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst, p]],{n,6!}];lst
%t Select[Prime[Range[100]], PrimeQ[(# + 1)^3 / 8 + (# - 1) / 2]&] (* _Vincenzo Librandi_, Apr 09 2013 *)
%o (Magma) [p: p in PrimesInInterval(3, 1200) | IsPrime((p+1)^3 div 8+(p-1) div 2)]; // _Vincenzo Librandi_, Apr 09 2013
%Y Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009
%E Edited by _R. J. Mathar_, Aug 24 2009
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