A341215 - OEIS

%I #12 Feb 07 2021 17:30:22

%S 5,7,11,19,29,31,37,43,53,113,127,163,173,199,257,271,317,353,397,439,

%T 457,461,557,599,659,757,809,991,997,1019,1069,1129,1289,1327,1439,

%U 1447,1549,1621,1733,1747,1759,1831,1913,2027,2113,2141,2153,2309,2339,2357,2383,2423,2473,2663,2741,2801

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

%H Robert Israel, <a href="/A341215/b341215.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 R:=  NULL: count:= 0:

%p q:= 2:

%p while count < 100 do

%p   p:= q; q:= nextprime(p);

%p   if isprime(2*p+3*q) and isprime(3*p+2*q) then

%p     count:= count+1; R:= R, p

%p   fi

%p od:

%p R;

%o (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 Contains A174922.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 06 2021