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%I #13 Jul 27 2013 10:29:01
%S 7,23,37,47,67,73,233,277,353,479,613,619,631,647,809,1009,1069,1097,
%T 1283,1297,1433,1453,1459,1471,1493,1499,1607,1613,1663,1709,1721,
%U 1759,1783,1789,1867,1889,1901,1931,1993,2099,2137,2161,2377,2383,2411,2521,2621
%N 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.
%C 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.
%e 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.
%p for i from 2 to 400 do
%p p := ithprime(i) ;
%p pn := prevprime(p) ;
%p pk := 2*p-pn ;
%p if isprime(pk) and pk > nextprime(p) then
%p printf("%d,",p) ;
%p else
%p pk := nextprime(p) ;
%p pn := 2*p-pk ;
%p if isprime(pn) and pn < prevprime(p) then
%p printf("%d,",p) ;
%p end if;
%p end if;
%p end do: # _R. J. Mathar_, Jul 20 2013
%Y Cf. A098029.
%K nonn
%O 1,1
%A _Irina Gerasimova_, Jul 11 2013
%E Corrected by _R. J. Mathar_, Jul 20 2013
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