A079024 Let p and q be two prime numbers, not necessarily consecutive, such that q - p = 2n; a(n) is the number of distinct partitions of 2n into even numbers so that each partition corresponds to a consecutive prime difference pattern (k-tuple) and p<=A000230(n). Multiple occurrences of a partition are not counted.

1, 2, 3, 5, 5, 12, 9, 17, 30, 29, 32, 79, 64, 70, 236, 116, 48, 342, 375, 359, 633, 310, 852, 846, 644, 354, 1048, 1191, 635, 1664, 539, 1127, 3971, 1656, 3022, 984, 3894, 2399, 4439, 6431, 2765, 10256, 1818, 5427, 10251, 8153, 9119, 7083, 6456, 5033

Offset: 1

Author

Labos Elemer, Jan 24 2003

Keywords

• nonn

Comments

In case of partitions enumerated in A079022-A079024 permutation if parts is relevant since may correspond to different possible consecutive prime-difference patterns.

Examples

			Only those and distinct partitions are counted which appear not later than prime A000230(n); n=7, d=14, A000230(7)=113, number of solutions to p+14=q, - both p and q are primes and p<=113 - is 9. This 9 distinct partitions and their introducing primes are as follows:3[2244], 5[24242], 17[2462], 23[626], 29[2642], 47[662], 83[68], 89[842], 113[14]=A000230(7).
		

Crossrefs

Cf. A000230, A079015-A079024.