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
Keywords
Examples
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.
Links
- J. Stauduhar, Table of n, a(n) for n = 1..5000
Programs
-
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 *)