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A335550 Number of minimal normal patterns avoided by the prime indices of n in increasing or decreasing order, counting multiplicity.

%I A335550 #8 Jun 27 2020 09:07:56
%S A335550 1,3,3,3,3,3,3,3,3,3,3,4,3,3,3,3,3,4,3,4,3,3,3,4,3,3,3,4,3,3,3,3,3,3,
%T A335550 3,3,3,3,3,4,3,3,3,4,4,3,3,4,3,4,3,4,3,4,3,4,3,3,3,4,3,3,4,3,3,3,3,4,
%U A335550 3,3
%N A335550 Number of minimal normal patterns avoided by the prime indices of n in increasing or decreasing order, counting multiplicity.
%C A335550 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.
%C A335550 We define a (normal) 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).
%H A335550 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335550 Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335550 It appears that for n > 1, a(n) = 3 if n is a power of a squarefree number (A072774), and a(n) = 4 otherwise.
%e A335550 The a(12) = 4 minimal patterns avoiding (1,1,2) are: (2,1), (1,1,1), (1,2,2), (1,2,3).
%e A335550 The a(30) = 3 minimal patterns avoiding (1,2,3) are: (1,1), (2,1), (1,2,3,4).
%Y A335550 The version for standard compositions is A335465.
%Y A335550 Patterns are counted by A000670.
%Y A335550 Sum of prime indices is A056239.
%Y A335550 Each number's prime indices are given in the rows of A112798.
%Y A335550 Patterns are ranked by A333217.
%Y A335550 Patterns matched by compositions are counted by A335456.
%Y A335550 Patterns matched by prime indices are counted by A335549.
%Y A335550 Patterns matched by partitions are counted by A335837.
%Y A335550 Cf. A124770, A124771, A181796, A269134, A299702, A333257, A335452, A335516.
%K A335550 nonn,more
%O A335550 1,2
%A A335550 _Gus Wiseman_, Jun 26 2020