A227421 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

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.

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) ;