

A224708


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


7



0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 1, 3, 1, 4, 2, 4, 2, 4, 2, 6, 3, 5, 3, 6, 4, 8, 5, 7, 5, 8, 5, 10, 6, 8, 7, 10, 7, 12, 8, 11, 8, 11, 8, 14, 9, 13, 9, 13, 10, 16, 11, 14, 11, 15, 12, 19, 13, 15, 13, 18, 13, 20, 14, 17, 15, 20, 15, 22, 16, 20, 16, 21
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OFFSET

1,12


COMMENTS

For n>11, a(n)>0.  Geoffrey Critzer, Jan 31 2015
Last occurrence of n is a(A014092(n+4)).  Anthony Browne, May 25 2016


LINKS

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


FORMULA

a(2n)  a(2n+1) + A010051(n) = A045917(n).  Anthony Browne, May 03 2016
a(A014092(n+4)) = n.  Anthony Browne, May 25 2016


EXAMPLE

For n=8, in the set {{7,1},{6,2},{5,3},{4,4}}, {4,4} is the only partition {a,b} where a and b are both composite, so a(8)=1.
For n=12, we have partitions {8,4} and {6,6}, so a(12)=2.


MATHEMATICA

nn = 76; Rest[Transpose[CoefficientList[Series[Product[1/(1  y x^i), {i, Select[Range[2, nn], ! PrimeQ[#] &]}], {x, 0, nn}], {x, y}]][[3]]] (* Geoffrey Critzer, Jan 31 2015 *)
f[n_] := Count[ PrimeQ@ Rest@ IntegerPartitions[ n, {2}], {False, False}]; Array[f, 76] (* Robert G. Wilson v, Feb 04 2015 *)


CROSSREFS

Cf. A014092, A010051, A045917.
Sequence in context: A326850 A303756 A105259 * A322023 A029229 A029216
Adjacent sequences: A224705 A224706 A224707 * A224709 A224710 A224711


KEYWORD

nonn


AUTHOR

J. Stauduhar, Apr 16 2013


STATUS

approved



