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A063713 Numbers n such that there exist primes p, q, r with n*2 = p - r = r + q (values of r are given in A063714. 3
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 30, 32, 33, 35, 36, 38, 39, 42, 43, 45, 46, 48, 50, 51, 52, 53, 54, 55, 57, 58, 60, 63, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 80, 81, 84, 85, 87, 88, 90, 93, 96, 97, 98, 99, 100, 101, 102, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

10*2 = 20 = 23 - 3 = 3 + 17, A063714(7) = 3; 11*2 = 22 = 41 - 19 = 19 + 3, A063714(8) = 19 28 is missing because we have the prime sums (Goldbach): 5 + 23 = 11 + 17 and differences with primes less 28: 31 - 3 = 41 - 13 = 47 - 19; none of these have a prime in common.

MAPLE

filter:= proc(n) local k;

  k:= 1;

  while k < 2*n do

    k:= nextprime(k);

    if isprime(2*n+k) and isprime(2*n-k) then return true fi

  od;

  false

end proc:

select(filter, [$1..1000]); # Robert Israel, Oct 09 2017

MATHEMATICA

okQ[n_] := AnyTrue[Prime[Range[PrimePi[2 n - 2]]], PrimeQ[2 n + #] && PrimeQ[2 n - #]&]; Select[Range[105], okQ] (* Jean-Fran├žois Alcover, Feb 12 2018 *)

CROSSREFS

Cf. A063714, A002373, A020483.

Sequence in context: A026425 A026440 A299487 * A026462 A039230 A111222

Adjacent sequences:  A063710 A063711 A063712 * A063714 A063715 A063716

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 10 2001

STATUS

approved

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Last modified October 20 16:08 EDT 2019. Contains 328268 sequences. (Running on oeis4.)