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

1,2

Comments

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

Links

Table of n, a(n) for n=1..50.

Example

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.

Sequence in context: A343395 A050368 A156834 * A357000 A342421 A319631

Adjacent sequences: A079021 A079022 A079023 * A079025 A079026 A079027

Keyword

nonn

Author

Labos Elemer, Jan 24 2003

Status

approved