A138170 - OEIS

%I #14 Apr 06 2023 16:25:49

%S 2,3,5,23,31,61,83,89,149,179,239,251,263,269,353,367,419,433,449,503,

%T 557,569,571,587,653,701,733,761,839,941,983,991,1109,1123,1187,1193

%N Prime numbers p1 such that p1*p2 + (p2 mod p1) is a prime, where p2 is the next prime after p1.

%C Prime numbers p1 such that p1*p2+p2-p1 is a prime, where p2 is the next prime after p1. - _J. M. Bergot_ and _Robert Israel_, Dec 30 2021

%H Harvey P. Dale, <a href="/A138170/b138170.txt">Table of n, a(n) for n = 1..1000</a>

%e 2 is prime, 3 is next prime, 2*3 + (3 mod 2) =  6 + 1 =  7;

%e 3 is prime, 5 is next prime, 3*5 + (5 mod 3) = 15 + 2 = 17;

%e 5 is prime, 7 is next prime, 5*7 + (7 mod 5) = 35 + 2 = 37.

%t a={};Do[p1=Prime[n];p2=Prime[n+1];e=p1*p2+Mod[p2,p1];If[PrimeQ[e],AppendTo[a,p1]],{n,10^2*2}];a

%t pnQ[n_]:=Module[{np=NextPrime[n]},PrimeQ[n*np+Mod[np,n]]]; Select[Prime[ Range[200]],pnQ] (* _Harvey P. Dale_, Mar 09 2014 *)

%t Select[Partition[Prime[Range[200]],2,1],PrimeQ[Times@@#+Mod[#[[2]],#[[1]]]]&][[;;,1]] (* _Harvey P. Dale_, Apr 06 2023 *)

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 06 2008