A224712 - OEIS

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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.

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 *)

Table[Count[IntegerPartitions[n, {2}], _?(FreeQ[#, 1]&&Total[Boole[ PrimeQ[ #]]] == 1&)], {n, 80}] (* Harvey P. Dale, Jul 21 2021 *)

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: A351886 A323901 A132223 * A363301 A135941 A036998

Adjacent sequences: A224709 A224710 A224711 * A224713 A224714 A224715

KEYWORD

nonn,easy

AUTHOR

J. Stauduhar, Apr 20 2013

STATUS

approved