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A341215 Primes p such that 2*p+3*q and 3*p+2*q are prime, where q is the next prime after p.

%I A341215 #14 Jun 11 2025 16:25:41
%S A341215 5,7,11,19,29,31,37,43,53,113,127,163,173,199,257,271,317,353,397,439,
%T A341215 457,461,557,599,659,757,809,991,997,1019,1069,1129,1289,1327,1439,
%U A341215 1447,1549,1621,1733,1747,1759,1831,1913,2027,2113,2141,2153,2309,2339,2357,2383,2423,2473,2663,2741,2801
%N A341215 Primes p such that 2*p+3*q and 3*p+2*q are prime, where q is the next prime after p.
%H A341215 Robert Israel, <a href="/A341215/b341215.txt">Table of n, a(n) for n = 1..10000</a>
%e A341215 a(3) = 11 is a term because the next prime is 13 and 2*11+3*13 = 61 and 3*11+2*13 = 59 are prime.
%p A341215 R:=  NULL: count:= 0:
%p A341215 q:= 2:
%p A341215 while count < 100 do
%p A341215   p:= q; q:= nextprime(p);
%p A341215   if isprime(2*p+3*q) and isprime(3*p+2*q) then
%p A341215     count:= count+1; R:= R, p
%p A341215   fi
%p A341215 od:
%p A341215 R;
%t A341215 Select[Partition[Prime[Range[500]],2,1],AllTrue[{2#[[1]]+3#[[2]],3#[[1]]+2#[[2]]},PrimeQ]&][[;;,1]] (* _Harvey P. Dale_, Jun 11 2025 *)
%o A341215 (PARI) isok(p) = isprime(p) && (q=nextprime(p+1)) && isprime(2*p+3*q) && isprime(3*p+2*q); \\ _Michel Marcus_, Feb 07 2021
%Y A341215 Contains A174922.
%K A341215 nonn
%O A341215 1,1
%A A341215 _J. M. Bergot_ and _Robert Israel_, Feb 06 2021