A293909 - OEIS

%I #17 Feb 16 2025 08:33:51

%S 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,

%T 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,

%U 4,8,6,7,10,5,5,11,3,7,10,5,7,9,5,5,13,8,5

%N 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.

%H Bert Dobbelaere, <a href="/A293909/b293909.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%e 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.

%Y Cf. A002375, A226237, A278700, A279103, A279315, A279481, A279727, A279728, A279729, A279792.

%K nonn,changed

%O 1,9

%A _Wesley Ivan Hurt_, Oct 19 2017

%E More terms from _Bert Dobbelaere_, Sep 15 2019