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 A335462 Number of (1,2,1) and (2,1,2)-matching permutations of the prime indices of n. 17
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,36 COMMENTS 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. We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1). LINKS Wikipedia, Permutation pattern EXAMPLE The a(n) permutations for n = 36, 72, 270, 144, 300: (1,2,1,2) (1,1,2,1,2) (2,1,2,3,2) (1,1,1,2,1,2) (1,2,3,1,3) (2,1,2,1) (1,2,1,1,2) (2,1,3,2,2) (1,1,2,1,1,2) (1,3,1,2,3) (1,2,1,2,1) (2,2,1,3,2) (1,1,2,1,2,1) (1,3,1,3,2) (2,1,1,2,1) (2,2,3,1,2) (1,2,1,1,1,2) (1,3,2,1,3) (2,1,2,1,1) (2,3,1,2,2) (1,2,1,1,2,1) (1,3,2,3,1) (2,3,2,1,2) (1,2,1,2,1,1) (2,1,3,1,3) (2,1,1,1,2,1) (2,3,1,3,1) (2,1,1,2,1,1) (3,1,2,1,3) (2,1,2,1,1,1) (3,1,2,3,1) (3,1,3,1,2) (3,1,3,2,1) (3,2,1,3,1) MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Table[Length[Select[Permutations[primeMS[n]], MatchQ[#, {___, x_, ___, y_, ___, x_, ___}/; xy]&]], {n, 100}] CROSSREFS The avoiding version is A333175. Replacing "and" with "or" gives A335460. Positions of nonzero terms are A335463. Permutations of prime indices are counted by A008480. Unsorted prime signature is A124010. Sorted prime signature is A118914. STC-numbers of permutations of prime indices are A333221. Patterns matched by standard compositions are counted by A335454. Dimensions of downsets of standard compositions are A335465. Cf. A056239, A056986, A112798, A158005, A181796, A335451, A335452. Sequence in context: A130779 A130706 A000038 * A353349 A349399 A228594 Adjacent sequences: A335459 A335460 A335461 * A335463 A335464 A335465 KEYWORD nonn AUTHOR Gus Wiseman, Jun 20 2020 STATUS approved

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Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)