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A335520
Number of (1,2,3)-matching permutations of the prime indices of n.
10
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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0
OFFSET
1,60
COMMENTS
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).
FORMULA
For n > 0, a(n) + A335521(n) = A008480(n).
EXAMPLE
The a(n) permutations for n = 30, 60, 120, 210, 180, 480:
(123) (1123) (11123) (1234) (11223) (1111123)
(1213) (11213) (1243) (11232) (1111213)
(1231) (11231) (1324) (12123) (1111231)
(12113) (1342) (12132) (1112113)
(12131) (1423) (12213) (1112131)
(12311) (2134) (12231) (1112311)
(2314) (12312) (1121113)
(2341) (12321) (1121131)
(3124) (21123) (1121311)
(4123) (21213) (1123111)
(21231) (1211113)
(1211131)
(1211311)
(1213111)
(1231111)
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_, ___, z_, ___}/; x<y<z]&]], {n, 100}]
CROSSREFS
Positions of nonzero terms are A000977.
These permutations are ranked by A335479.
These compositions are counted by A335514.
Patterns matching this pattern are counted by A335515.
The complement A335521 is the avoiding version.
Permutations of prime indices are counted by A008480.
Patterns are counted by A000670 and ranked by A333217.
Anti-run permutations of prime indices are counted by A335452.
Sequence in context: A051344 A236534 A101856 * A326291 A269250 A334740
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 19 2020
STATUS
approved