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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.

%I A227421 #13 Jul 27 2013 10:29:01
%S A227421 7,23,37,47,67,73,233,277,353,479,613,619,631,647,809,1009,1069,1097,
%T A227421 1283,1297,1433,1453,1459,1471,1493,1499,1607,1613,1663,1709,1721,
%U A227421 1759,1783,1789,1867,1889,1901,1931,1993,2099,2137,2161,2377,2383,2411,2521,2621
%N 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.
%C A227421 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 A227421 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 A227421 for i from 2 to 400 do
%p A227421     p := ithprime(i) ;
%p A227421     pn := prevprime(p) ;
%p A227421     pk := 2*p-pn ;
%p A227421     if isprime(pk) and pk > nextprime(p) then
%p A227421         printf("%d,",p) ;
%p A227421     else
%p A227421         pk := nextprime(p) ;
%p A227421         pn := 2*p-pk ;
%p A227421         if isprime(pn) and pn < prevprime(p) then
%p A227421             printf("%d,",p) ;
%p A227421         end if;
%p A227421     end if;
%p A227421 end do: # _R. J. Mathar_, Jul 20 2013
%Y A227421 Cf. A098029.
%K A227421 nonn
%O A227421 1,1
%A A227421 _Irina Gerasimova_, Jul 11 2013
%E A227421 Corrected by _R. J. Mathar_, Jul 20 2013