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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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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) ;         end if;     end if; end do: # R. J. Mathar, Jul 20 2013 CROSSREFS Cf. A098029. Sequence in context: A329931 A157811 A341284 * A098029 A098039 A132237 Adjacent sequences:  A227418 A227419 A227420 * A227422 A227423 A227424 KEYWORD nonn AUTHOR Irina Gerasimova, Jul 11 2013 EXTENSIONS Corrected by R. J. Mathar, Jul 20 2013 STATUS approved

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Last modified September 19 17:35 EDT 2021. Contains 347564 sequences. (Running on oeis4.)