

A293909


Number of Goldbach partitions (p,q) of 2n, p <= q, such that both 2n2 and 2n+2 have a Goldbach partition with a greater difference between its prime parts than qp.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,9


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


EXAMPLE

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 133 = 10 and 173 = 14 are the largest differences of the primes among the Goldbach partitions of 2n2 and 2n+2. The Goldbach partitions of 2(9) = 18 are 13+5 = 11+7. Since 135 = 8 and 117 = 4 are both less than min(10,14) = 10, a(9) = 2.


CROSSREFS

Cf. A002375, A226237, A278700, A279103, A279315, A279481, A279727, A279728, A279729, A279792.
Sequence in context: A175328 A338776 A198325 * A002850 A111944 A109814
Adjacent sequences: A293906 A293907 A293908 * A293910 A293911 A293912


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, Oct 19 2017


EXTENSIONS

More terms from Bert Dobbelaere, Sep 15 2019


STATUS

approved



