A137724 - OEIS

%I #16 Jan 09 2024 10:49:22

%S 37,181,397,757,829,1657,2089,2161,2341,3061,5077,6337,7057,7309,7561,

%T 8389,9109,9829,10369,10729,13789,17137,21061,21817,21961,23869,24517,

%U 24877,25237,26209,28297,29269,31177,31249,32077,32257,33049,33301,35281,38377,39709,41221,42337,44641,47161

%N Prime numbers p such that p +- ((p-1)/6) are primes.

%H Vincenzo Librandi, <a href="/A137724/b137724.txt">Table of n, a(n) for n = 1..1000</a>

%e 37+-6 = primes,

%e 181+-30 = primes,

%e 397+-(396/6) = primes.

%t w=6;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) / 6]&& PrimeQ[# - (# - 1) / 6] &] (* _Vincenzo Librandi_, Jun 15 2013 °)

%t Select[Prime[Range[5000]],AllTrue[#+{(#-1)/6,-(#-1)/6},PrimeQ]&] (* _Harvey P. Dale_, Jan 09 2024 *)

%o (Magma) [p: p in PrimesInInterval(5, 50000)| IsPrime((7*p-1) div 6 ) and IsPrime((5*p+1) div 6)]; // _Vincenzo Librandi_, Jun 15 2013

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2008