cp's OEIS Frontend

A335463 Numbers k such that there exists a permutation of the prime indices of k matching both (1,2,1) and (2,1,2).

%I A335463 #12 Feb 09 2021 01:55:52
%S A335463 36,72,90,100,108,126,144,180,196,198,200,216,225,234,252,270,288,300,
%T A335463 306,324,342,350,360,378,392,396,400,414,432,441,450,468,484,500,504,
%U A335463 522,525,540,550,558,576,588,594,600,612,630,648,650,666,675,676,684,700
%N A335463 Numbers k such that there exists a permutation of the prime indices of k matching both (1,2,1) and (2,1,2).
%C A335463 A prime index of k is a number m such that prime(m) divides k. The multiset of prime indices of k is row k of A112798.
%C A335463 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).
%H A335463 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335463 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%e A335463 The sequence of terms together with their prime indices begins:
%e A335463    36: {1,1,2,2}
%e A335463    72: {1,1,1,2,2}
%e A335463    90: {1,2,2,3}
%e A335463   100: {1,1,3,3}
%e A335463   108: {1,1,2,2,2}
%e A335463   126: {1,2,2,4}
%e A335463   144: {1,1,1,1,2,2}
%e A335463   180: {1,1,2,2,3}
%e A335463   196: {1,1,4,4}
%e A335463   198: {1,2,2,5}
%e A335463   200: {1,1,1,3,3}
%e A335463   216: {1,1,1,2,2,2}
%e A335463   225: {2,2,3,3}
%e A335463   234: {1,2,2,6}
%e A335463   252: {1,1,2,2,4}
%e A335463   270: {1,2,2,2,3}
%e A335463   288: {1,1,1,1,1,2,2}
%e A335463   300: {1,1,2,3,3}
%t A335463 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335463 Select[Range[100],Select[Permutations[primeMS[#]],MatchQ[#,{___,x_,___,y_,___,x_,___}/;x<y]&&MatchQ[#,{___,x_,___,y_,___,x_,___}/;x>y]&]!={}&]
%Y A335463 Replacing "and" with "or" gives A126706.
%Y A335463 Positions of nonzero terms in A335462.
%Y A335463 Permutations of prime indices are counted by A008480.
%Y A335463 Unsorted prime signature is A124010. Sorted prime signature is A118914.
%Y A335463 STC-numbers of permutations of prime indices are A333221.
%Y A335463 Patterns matched by standard compositions are counted by A335454.
%Y A335463 Cf. A056239, A056986, A112798, A158005, A181796, A333175, A335451, A335452, A335460, A335465.
%K A335463 nonn
%O A335463 1,1
%A A335463 _Gus Wiseman_, Jun 20 2020