A098029 -id:A098029 - cp's OEIS frontend

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

Irina Gerasimova, Jul 11 2013

nonn

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.

			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.

Cf. A098029.

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

Corrected by R. J. Mathar, Jul 20 2013

cp's OEIS Frontend

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.

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