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A224712 The number of unordered partitions {a, b} of n such that a or b is composite and the other is prime. 5
0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 4, 2, 3, 2, 4, 2, 6, 2, 5, 3, 6, 3, 8, 2, 7, 4, 9, 5, 9, 3, 8, 6, 9, 4, 11, 3, 11, 8, 10, 6, 12, 4, 11, 7, 12, 7, 14, 4, 13, 7, 15, 9, 15, 5, 14, 10, 16, 9, 16, 4, 15, 12, 16, 8, 18, 6, 18, 14, 17, 9, 19, 7, 18, 11, 19, 11, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

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

EXAMPLE

For n = 6, in the set {{5, 1}, {4, 2}, {3, 3}}, {4, 2} is the only partition that satisfies the requirements, so a(6) = 1.

For n = 9, we have partitions {6, 3} and {5, 4}, so a(9) = 2.

MATHEMATICA

Table[Length[Select[Range[2, Floor[n/2]], (PrimeQ[#] && Not[PrimeQ[n - #]]) || (Not[PrimeQ[#]] && PrimeQ[n - #]) &]], {n, 80}] (* Alonso del Arte, Apr 21 2013 *)

PROG

(PARI) a(n)=my(s); forprime(p=2, n-4, s+=!isprime(n-p)); s \\ Charles R Greathouse IV, Apr 30 2013

CROSSREFS

Cf. A062602 (allows 1 as well as composites), A224708 (a and b are both composite).

Sequence in context: A208569 A323901 A132223 * A135941 A036998 A121464

Adjacent sequences:  A224709 A224710 A224711 * A224713 A224714 A224715

KEYWORD

nonn,easy

AUTHOR

J. Stauduhar, Apr 20 2013

STATUS

approved

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Last modified September 18 20:55 EDT 2019. Contains 327181 sequences. (Running on oeis4.)