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 A326255 MM-numbers of capturing multiset partitions. 15
 667, 989, 1334, 1633, 1769, 1817, 1978, 2001, 2021, 2323, 2461, 2599, 2623, 2668, 2967, 2987, 3197, 3266, 3335, 3538, 3634, 3713, 3749, 3956, 3979, 4002, 4042, 4163, 4171, 4331, 4379, 4429, 4439, 4577, 4646, 4669, 4747, 4819, 4859, 4899, 4922, 4945, 5029, 5198 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS First differs from A326256 in having 2599. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is obtained by taking the multiset of prime indices of each prime index of n. A multiset partition is capturing if it has two blocks of the form {...x...y...} and {...z...t...} where x < z and t < y or z < x and y < t. This is a weaker condition than nesting, so for example {{1,3,5},{2,4}} is capturing but not nesting. LINKS EXAMPLE The sequence of terms together with their multiset multisystems begins:    667: {{2,2},{1,3}}    989: {{2,2},{1,4}}   1334: {{},{2,2},{1,3}}   1633: {{2,2},{1,1,3}}   1769: {{1,3},{1,2,2}}   1817: {{2,2},{1,5}}   1978: {{},{2,2},{1,4}}   2001: {{1},{2,2},{1,3}}   2021: {{1,4},{2,3}}   2323: {{2,2},{1,6}}   2461: {{2,2},{1,1,4}}   2599: {{2,2},{1,2,3}}   2623: {{1,4},{1,2,2}}   2668: {{},{},{2,2},{1,3}}   2967: {{1},{2,2},{1,4}}   2987: {{1,3},{2,2,2}}   3197: {{2,2},{1,7}}   3266: {{},{2,2},{1,1,3}}   3335: {{2},{2,2},{1,3}}   3538: {{},{1,3},{1,2,2}} MATHEMATICA capXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; xt||x>z&&yTable[PrimePi[p], {k}]]]]; Select[Range[10000], capXQ[primeMS/@primeMS[#]]&] CROSSREFS MM-numbers of crossing multiset partitions are A324170. MM-numbers of nesting multiset partitions are A326256. MM-numbers of crossing capturing multiset partitions are A326259. Capturing set partitions are A326243. Cf. A001055, A034827, A058681, A112798, A117662, A122880, A302242. Cf. A326211, A326249, A326254, A326257, A326258. Sequence in context: A328551 A172922 A046694 * A326256 A210477 A138563 Adjacent sequences:  A326252 A326253 A326254 * A326256 A326257 A326258 KEYWORD nonn AUTHOR Gus Wiseman, Jun 20 2019 STATUS approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)