A352100 - OEIS

%I #10 Feb 16 2025 08:34:03

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

%T 11,15,13,12,14,14,13,16,16,13,17,18,14,19,19,17,22,19,18,21,21,19,22,

%U 21,19,23,24,18,27,26,22,29,26,24,28,29,27,28,28,25,31,32,26,34,31

%N Number of partitions of 2n into two odd parts that are not both prime.

%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>

%F a(1) = a(2) = 1, a(n) = ceiling(n/2) - A045917(n), n >= 3.

%e a(17) = 5; There are 5 partitions of 2*17 = 34 into two odd parts that are not both prime: 34 = 1+33 = 7+27 = 9+25 = 13+21 = 15+19.

%t a[1] = a[2] = 1; a[n_] := Ceiling[n/2] - Count[2*n - Prime[Range[PrimePi[n]]], _?PrimeQ]; Array[a, 100] (* _Amiram Eldar_, May 12 2022 *)

%Y Cf. A045917.

%K nonn,changed

%O 1,6

%A _Wesley Ivan Hurt_, May 05 2022