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URL: https://oeis.org/A224709

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A224709
The number of unordered partitions {a,b} of the even numbers 2n such that a and b are composite.
2
0, 0, 0, 1, 1, 2, 2, 3, 4, 4, 4, 6, 5, 6, 8, 7, 8, 10, 8, 10, 12, 11, 11, 14, 13, 13, 16, 14, 15, 19, 15, 18, 20, 17, 20, 22, 20, 21, 24, 22, 22, 27, 23, 24, 30, 25, 26, 30, 27, 30, 33, 30, 30, 34, 32, 33, 37, 33, 33, 41, 33, 36, 42, 36, 40, 43, 39, 40, 44
OFFSET
1,6
COMMENTS
Conjecture: a(3n+9) > a(3n+8) and a(3n+10) < a(3n+9) for n>=1. - Anthony Browne, Jun 26 2016
LINKS
FORMULA
a(n) = Sum_{k=1..n-1} (1-A010051(k+1))(1-A010051(2n-k-1)). - Anthony Browne, Jun 26 2016
EXAMPLE
For n=6, 2*6=12 and the partitions of 12 are (1,11),(2,10),(3,9),(4,8),(5,7),(6,6). Of these, 2 are composite pairs, namely (4,8),(6,6) so a(6)=2.
MATHEMATICA
Table[Count[Transpose@ {#, 2 n - #} &@ Range@ n, w_ /; Times @@ Boole@ Map[CompositeQ, w] > 0], {n, 69}] (* Michael De Vlieger, Jun 26 2016 *)
PROG
(PARI) a(n) = sum(k=1, n-1, (1-isprime(k+1))*(1-isprime(2*n-k-1))); \\ Michel Marcus, Apr 11 2022
CROSSREFS
Subsequence of A224708.
Cf. A010051.
Sequence in context: A284511 A262976 A349608 * A309965 A366385 A070172
KEYWORD
nonn
AUTHOR
J. Stauduhar, Apr 16 2013
STATUS
approved