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A339414 Primes p such that (p+q)/4 is prime, where q is the next prime after p.

%I A339414 #15 Dec 05 2020 18:14:57
%S A339414 3,5,23,31,83,131,251,271,331,383,443,563,971,1123,1223,1231,1283,
%T A339414 1291,1543,2063,2371,2383,2551,2851,2903,2963,3083,3323,3691,3889,
%U A339414 4051,4283,4591,4733,4831,4871,4951,5003,5209,5351,5683,5711,5851,6229,6271,6323,6491,6863,6911,7393,7451,7583,7643
%N A339414 Primes p such that (p+q)/4 is prime, where q is the next prime after p.
%C A339414 After the initial 2 terms, a(n)=2*A118134(n)-3. - _Hugo Pfoertner_, Dec 03 2020
%H A339414 Robert Israel, <a href="/A339414/b339414.txt">Table of n, a(n) for n = 1..10000</a>
%e A339414 a(5)=83 is in the sequence because it is prime, the next prime is 89, and (83+89)/4 = 43 is prime.
%p A339414 P:= select(isprime, [seq(i,i=3..10000,2)]):
%p A339414 R:= (P[1..-2]+P[2..-1])/4:
%p A339414 P[select(i-> R[i]::integer and isprime(R[i]), [$1..nops(R)])];
%o A339414 (PARI) isok(p) = isprime(p) && iferr(isprime((p+nextprime(p+1))/4),E,0); \\ _Michel Marcus_, Dec 04 2020
%Y A339414 Subset of A098058.
%Y A339414 Cf. A118134.
%K A339414 nonn
%O A339414 1,1
%A A339414 _Robert Israel_, Dec 03 2020