A227421 - OEIS

%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