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

5, 37, 53, 157, 173, 233, 257, 277, 353, 373, 401, 593, 613, 653, 733, 769, 977, 1097, 1297, 1433, 1493, 1613, 1753, 1993, 2137, 2161, 2377, 2417, 2677, 2693, 2749, 2797, 3313, 3533, 3637, 3733, 4013, 4133, 4457, 4513

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 26 2014

Keywords

• nonn

Comments

All terms must necessarily be primes of form 4n+1. - Jens Kruse Andersen, Jul 15 2014

Examples

			5 is in this sequence because (A002145(1) + A002145(2))/2 = (3 + 7)/2 = 5 and 5 is prime.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A002145, A071680.

Programs

Maple

N:= 10000; # get all entries <= N
P3:= select(isprime,[seq(4*i+3,i=0..floor((N-3)/4))]):
select(isprime,[seq((P3[i]+P3[i+1])/2, i=1..nops(P3)-1)]); # Robert Israel, Jul 15 2014

PARI

p=[]; forstep(n=3, 5000, 4, if(isprime(n), p=concat(p, n))); p;
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

Extensions

One term deleted and another term inserted by Colin Barker, Jun 27 2014