A224710 The number of unordered partitions {a,b} of 2n-1 such that a and b are composite.

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 29, 30, 31, 32, 33, 33, 34, 34, 35, 36, 36

Offset: 1

Author

J. Stauduhar, Apr 16 2013

Keywords

• nonn

Comments

Except for the initial terms, the same sequence as A210469.

Examples

			n=7: 13 has a unique representation as the sum of two composite numbers, namely 13 = 4+9, so a(7)=1.
		

Links

• J. Stauduhar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A224708. Cf. A210469.

Programs

Mathematica

Table[Length@ Select[IntegerPartitions[2 n - 1, {2}] /. n_Integer /; ! CompositeQ@ n -> Nothing, Length@ # == 2 &], {n, 71}] (* Version 10.2, or *)
Table[If[n == 1, 0, n - 2 - PrimePi[2 n - 4]], {n, 71}] (* Michael De Vlieger, May 03 2016 *)

Formula

a(n) = n - 2 - primepi(2n-4) for n>1. - Anthony Browne, May 03 2016

a(A104275(n+2) + 1) = n. - Anthony Browne, May 25 2016