A352100 Number of partitions of 2n into two odd parts that are not both prime.

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, 11, 15, 13, 12, 14, 14, 13, 16, 16, 13, 17, 18, 14, 19, 19, 17, 22, 19, 18, 21, 21, 19, 22, 21, 19, 23, 24, 18, 27, 26, 22, 29, 26, 24, 28, 29, 27, 28, 28, 25, 31, 32, 26, 34, 31

Offset

1,6

Links

Table of n, a(n) for n=1..77.

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

Formula

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

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A045917.

Sequence in context: A216503 A216672 A104055 * A216200 A376696 A157873

Adjacent sequences: A352097 A352098 A352099 * A352101 A352102 A352103

Keyword

nonn

Author

Wesley Ivan Hurt, May 05 2022

Status

approved