A137770 - OEIS

%I #13 Sep 08 2022 08:45:33

%S 211,673,883,1093,1303,2731,7561,8443,10711,13063,14323,15373,16843,

%T 18523,24571,30703,31081,31963,36541,36583,40111,41161,42043,43051,

%U 44563,44773,55441,63421,64891,65563,67411,68041,70393,71233,74551,75391,79843

%N Prime numbers p such that p +- ((p-1)/7) are primes.

%H Vincenzo Librandi, <a href="/A137770/b137770.txt">Table of n, a(n) for n = 1..1000</a>

%e 211+-30 = primes;

%e 673+-(672/7) = primes.

%t w=7;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[80000]], PrimeQ[# + (# - 1) / 7] && PrimeQ[# - (# - 1) / 7] &] (* _Vincenzo Librandi_, Jun 15 2013 *)

%o (Magma) [p: p in PrimesInInterval(5, 80000)| IsPrime((8*p-1) div 7 ) and IsPrime((6*p+1) div 7)]; // _Vincenzo Librandi_, Jun 15 2013

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2008