login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335449 Number of (1,2,1)-avoiding permutations of the prime indices of n. 7
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 3, 2, 2, 1, 4, 2, 2, 2, 2, 1, 6, 1, 2, 2, 1, 2, 6, 1, 2, 2, 6, 1, 3, 1, 2, 3, 2, 2, 6, 1, 2, 1, 2, 1, 6, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Depends only on unsorted prime signature (A124010), but not only on sorted prime signature (A118914).

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. 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

Table of n, a(n) for n=1..87.

Wikipedia, Permutation pattern

Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.

EXAMPLE

The a(n) permutations for n = 2, 10, 36, 54, 324, 30, 1458, 90:

  (1)  (13)  (1122)  (1222)  (112222)  (123)  (1222222)  (1223)

       (31)  (2112)  (2122)  (211222)  (132)  (2122222)  (1322)

             (2211)  (2212)  (221122)  (213)  (2212222)  (2123)

                     (2221)  (222112)  (231)  (2221222)  (2213)

                             (222211)  (312)  (2222122)  (2231)

                                       (321)  (2222212)  (3122)

                                              (2222221)  (3212)

                                                         (3221)

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_, ___}/; x<y]&]], {n, 100}]

CROSSREFS

The matching version is A335446.

Patterns are counted by A000670.

(1,2,1)-avoiding patterns are counted by A001710.

Permutations of prime indices are counted by A008480.

Unsorted prime signature is A124010. Sorted prime signature is A118914.

(1,2,1) and (2,1,2)-avoiding permutations of prime indices are counted by A333175.

STC-numbers of permutations of prime indices are A333221.

(1,2,1) and (2,1,2)-avoiding permutations of prime indices are A335448.

Patterns matched by standard compositions are counted by A335454.

(1,2,1) or (2,1,2)-matching permutations of prime indices are A335460.

(1,2,1) and (2,1,2)-matching permutations of prime indices are A335462.

Dimensions of downsets of standard compositions are A335465.

(1,2,1)-avoiding compositions are ranked by A335467.

(1,2,1)-avoiding compositions are counted by A335471.

Cf. A056239, A056986, A112798, A158005, A181796, A335452, A335463.

Sequence in context: A121382 A305150 A333145 * A318464 A051265 A008647

Adjacent sequences:  A335446 A335447 A335448 * A335450 A335451 A335452

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 14 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)