A293909 Number of Goldbach partitions (p,q) of 2n, p <= q, such that both 2n-2 and 2n+2 have a Goldbach partition with a greater difference between its prime parts than q-p.

0, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 1, 3, 3, 2, 2, 4, 2, 3, 5, 3, 2, 5, 2, 3, 6, 2, 4, 5, 2, 4, 6, 4, 4, 6, 4, 4, 8, 4, 3, 9, 3, 4, 4, 3, 3, 8, 4, 5, 8, 5, 6, 10, 5, 5, 10, 4, 4, 8, 3, 5, 9, 5, 4, 8, 6, 7, 10, 5, 5, 11, 3, 7, 10, 5, 7, 9, 5, 5, 13, 8, 5

Offset: 1

Author

Wesley Ivan Hurt, Oct 19 2017

Keywords

• nonn

Examples

			a(9) = 2; Both 2(9)-2 = 16 and 2(9)+2 = 20 have two Goldbach partitions: 16 = 13+3 = 11+5 and 20 = 17+3 = 13+7. Note that 13-3 = 10 and 17-3 = 14 are the largest differences of the primes among the Goldbach partitions of 2n-2 and 2n+2. The Goldbach partitions of 2(9) = 18 are 13+5 = 11+7. Since 13-5 = 8 and 11-7 = 4 are both less than min(10,14) = 10, a(9) = 2.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..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. A002375, A226237, A278700, A279103, A279315, A279481, A279727, A279728, A279729, A279792.

Extensions

More terms from Bert Dobbelaere, Sep 15 2019