login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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*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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)