

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
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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*ppn ;
if isprime(pk) and pk > nextprime(p) then
printf("%d, ", p) ;
else
pk := nextprime(p) ;
pn := 2*ppk ;
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: A287309 A275777 A157811 * 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



