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%I #14 Sep 08 2022 08:45:33
%S 1489,2377,2689,2857,3361,3889,4969,5569,6481,6577,7537,8089,10009,
%T 11257,14281,14449,14929,15601,16057,17569,18121,19249,21817,22441,
%U 24169,24697,25057,26881,27481,30937,31081,33289,33409,33529,33961,36097,39841
%N Prime numbers p such that p +- ((p-1)/4) are primes.
%H Vincenzo Librandi, <a href="/A137705/b137705.txt">Table of n, a(n) for n = 1..1000</a>
%e 1489+1488/4 = 1861 and 1489-1488/4 = 1117, which are primes;
%e 2377+2376/4 = 2971 and 2377-2376/4 = 1783, which are primes.
%t w=4;s="";For[i=1,i<10^3*2,p=Prime[i];If[PrimeQ[p-((p-1)/w)]&&PrimeQ[p+((p-1)/w)],(*Print[p,":",p-((p-1)/w),",",p+((p-1)/w)];*)s=s<>ToString[p]<>","];i++ ];Print[s]
%t Select[Prime[Range[50000]], PrimeQ[# + (# - 1) / 4]&& PrimeQ[# - (# - 1) / 4] &] (* _Vincenzo Librandi_, Jun 15 2013 *)
%o (Magma) [p: p in PrimesInInterval(5, 40000)| IsPrime((5*p-1) div 4 ) and IsPrime((3*p+1) div 4)]; // _Vincenzo Librandi_, Jun 15 2013
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2008
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