cp's OEIS Frontend

A244374 Primes which are the arithmetic mean of two consecutive primes of the form 4n+3.

%I A244374 #29 Jul 17 2014 19:47:58
%S A244374 5,37,53,157,173,233,257,277,353,373,401,593,613,653,733,769,977,1097,
%T A244374 1297,1433,1493,1613,1753,1993,2137,2161,2377,2417,2677,2693,2749,
%U A244374 2797,3313,3533,3637,3733,4013,4133,4457,4513
%N A244374 Primes which are the arithmetic mean of two consecutive primes of the form 4n+3.
%C A244374 All terms must necessarily be primes of form 4n+1. - _Jens Kruse Andersen_, Jul 15 2014
%H A244374 Jens Kruse Andersen, <a href="/A244374/b244374.txt">Table of n, a(n) for n = 1..10000</a>
%e A244374 5 is in this sequence because (A002145(1) + A002145(2))/2 = (3 + 7)/2 = 5 and 5 is prime.
%p A244374 N:= 10000; # get all entries <= N
%p A244374 P3:= select(isprime,[seq(4*i+3,i=0..floor((N-3)/4))]):
%p A244374 select(isprime,[seq((P3[i]+P3[i+1])/2, i=1..nops(P3)-1)]); # _Robert Israel_, Jul 15 2014
%o A244374 (PARI)
%o A244374 p=[]; forstep(n=3, 5000, 4, if(isprime(n), p=concat(p, n))); p;
%o A244374 s=[]; for(k=1, #p-1, if(isprime(q=(p[k]+p[k+1])\2), s=concat(s, q))); s \\ _Colin Barker_, Jun 27 2014
%Y A244374 Cf. A002144, A002145, A071680.
%K A244374 nonn
%O A244374 1,1
%A A244374 _Juri-Stepan Gerasimov_, Jun 26 2014
%E A244374 One term deleted and another term inserted by _Colin Barker_, Jun 27 2014