A227421 Primes p such that 2*p = prime(m) + prime(m + k) for some k > 2, where prime(m) and p or p and prime(m + k) are consecutive primes.

7, 23, 37, 47, 67, 73, 233, 277, 353, 479, 613, 619, 631, 647, 809, 1009, 1069, 1097, 1283, 1297, 1433, 1453, 1459, 1471, 1493, 1499, 1607, 1613, 1663, 1709, 1721, 1759, 1783, 1789, 1867, 1889, 1901, 1931, 1993, 2099, 2137, 2161, 2377, 2383, 2411, 2521, 2621

Offset: 1

Author

Irina Gerasimova, Jul 11 2013

Keywords

• nonn

Comments

This is the middle prime q in a prime triple p < q=(p+r)/2 < r such that either (p,q) are two consecutive primes or (q,r) are two consecutive primes, but (p,q,r) are not three consecutive primes.

Examples

			In the ordered set of primes we have ...,607, 613, 617, 619, 631,... and (607 + 631)/2 = 619, where 619 and 631 are consecutive primes, therefore 619 is in this sequence.
		

Crossrefs

Cf. A098029.

Programs

Maple

for i from 2 to 400 do
    p := ithprime(i) ;
    pn := prevprime(p) ;
    pk := 2*p-pn ;
    if isprime(pk) and pk > nextprime(p) then
        printf("%d,",p) ;
    else
        pk := nextprime(p) ;
        pn := 2*p-pk ;
        if isprime(pn) and pn < prevprime(p) then
            printf("%d,",p) ;
        end if;
    end if;
end do: # R. J. Mathar, Jul 20 2013

Extensions

Corrected by R. J. Mathar, Jul 20 2013