A234345 Smallest q such that n <= q < 2n with p, q both prime, p+q = 2n, and p <= q.

2, 3, 5, 5, 7, 7, 11, 11, 13, 11, 13, 13, 17, 17, 19, 17, 19, 19, 23, 23, 31, 23, 29, 31, 29, 31, 37, 29, 31, 31, 41, 37, 37, 41, 41, 37, 47, 41, 43, 41, 43, 43, 47, 47, 61, 47, 53, 61, 53, 59, 61, 53, 61, 67, 59, 61, 73, 59, 61, 61, 71, 67, 67, 71, 71, 67, 83, 71, 73, 71, 73, 73

Offset: 2

Author

Wesley Ivan Hurt, Dec 23 2013

Keywords

• nonn
• easy

Comments

Also, the larger part in the Goldbach partition of 2n with the smallest difference between its prime parts.

Examples

			a(9) = 11; the Goldbach partitions of 2(9) = 18 are (13,5) and (11,7).  The partition with smaller difference between the primes is (11,7) (difference 4) and the larger part of this partition is 11.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture
• Index entries for sequences related to partitions

Crossrefs

Cf. A112823.

Programs

Mathematica

f[n_] := Block[{p = n/2}, While[! PrimeQ[p] || ! PrimeQ[n - p], p--];
  n - p]; Table[f[n], {n, 4, 146, 2}]

PARI

a(n) = {my(q = nextprime(n)); while (!isprime(2*n-q), q = nextprime(q+1)); q;} \\ Michel Marcus, Oct 22 2016

Formula

a(n) = 2n - A112823(n).