

A224710


The number of unordered partitions {a,b} of 2n1 such that a and b are composite.


2



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
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OFFSET

1,10


COMMENTS

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


LINKS

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


FORMULA

a(n) = n  2  primepi(2n4) for n>1.  Anthony Browne, May 03 2016
a(A104275(n+2) + 1) = n.  Anthony Browne, May 25 2016


EXAMPLE

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


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 *)


CROSSREFS

Subsequence of A224708. Cf. A210469.
Sequence in context: A194223 A194251 A029114 * A210469 A073174 A107631
Adjacent sequences: A224707 A224708 A224709 * A224711 A224712 A224713


KEYWORD

nonn


AUTHOR

J. Stauduhar, Apr 16 2013


STATUS

approved



