A224715 The number of unordered partitions {a,b} of prime(n) such that a or b is a nonnegative composite and the other is prime.

0, 0, 0, 1, 4, 3, 6, 5, 8, 9, 8, 11, 12, 11, 14, 15, 16, 15, 18, 19, 18, 21, 22, 23, 24, 25, 24, 27, 26, 29, 30, 31, 32, 31, 34, 33, 36, 37, 38, 39, 40, 39, 42, 41, 44, 43, 46, 47, 48, 47, 50, 51, 50, 53, 54, 55, 56, 55, 58, 59, 58, 61, 62, 63, 62, 65, 66

Offset

1,5

Links

J. Stauduhar, Table of n, a(n) for n = 1..5000

Example

For n = 5, prime(5) = 11. The pairwise partitions of 11 are {{10, 1}, {9, 2}, {8, 3}, {7, 4}, {6, 5}} and four partitions meet the requirements: {9, 2}, {8, 3}, {7, 4}, {6, 5}, so a(5) =  4.

Mathematica

nn = 100; mx = Prime[nn]; ps = Prime[Range[nn]]; notPs = Complement[Range[2, mx], ps]; t2 = Table[0, {Range[mx]}]; Do[s = i + j; If[s <= mx, t2[[s]]++], {i, ps}, {j, notPs}];  t2[[ps]] (* T. D. Noe, Apr 23 2013 *)

Crossrefs

Subsequence of A224712.

Essentially the same as A062302.

Sequence in context: A242554 A219176 A251739 * A062302 A261723 A362449

Adjacent sequences: A224712 A224713 A224714 * A224716 A224717 A224718

Keyword

nonn

Author

J. Stauduhar, Apr 22 2013

Status

approved