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A244374
Primes which are the arithmetic mean of two consecutive primes of the form 4n+3.
1
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
1,1
COMMENTS
All terms must necessarily be primes of form 4n+1. - Jens Kruse Andersen, Jul 15 2014
LINKS
EXAMPLE
5 is in this sequence because (A002145(1) + A002145(2))/2 = (3 + 7)/2 = 5 and 5 is prime.
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
One term deleted and another term inserted by Colin Barker, Jun 27 2014
STATUS
approved