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 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. 9
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 * A342421 A319631 A097453 Adjacent sequences:  A079021 A079022 A079023 * A079025 A079026 A079027 KEYWORD nonn AUTHOR Labos Elemer, Jan 24 2003 STATUS approved

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Last modified September 18 01:39 EDT 2021. Contains 347504 sequences. (Running on oeis4.)