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%I #15 Apr 24 2021 20:43:18
%S 5,29,47,139,293,557,607,647,659,709,773,809,811,863,1117,1171,1187,
%T 1801,2129,2467,2477,2549,2917,3023,3229,3329,3389,3469,3593,3617,
%U 3833,4261,4363,5791,5849,6269,6781,6949,7069,7703,8273,9397,9973,10141,10343,10369,10529,10657,11059,11329,13063
%N Primes p such that (3*p+q)/2 and (p+3*q)/2 are prime, where q is the next prime after p.
%C Intersection with A001359 is A069142.
%H Robert Israel, <a href="/A329151/b329151.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3)=47 is a term because it is prime, the next prime is 53, and (3*47+53)/2 = 97 and (47+3*53)/2 = 103 are both prime.
%p Primes:= [seq(ithprime(i),i=1..10000)]:
%p Res:= NULL:
%p for i from 2 to nops(Primes)-1 do
%p p:= Primes[i]; q:= Primes[i+1]; c:= (p+q)/2;
%p if isprime(p+c) and isprime(q+c) then
%p Res:= Res, p
%p fi
%p od:
%p Res;
%Y Cf. A001359, A069142.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Feb 25 2020
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