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A333218 Numbers k such that the k-th composition in standard order is a permutation (of an initial interval).

%I A333218 #9 Mar 17 2020 21:18:03
%S A333218 0,1,5,6,37,38,41,44,50,52,549,550,553,556,562,564,581,582,593,600,
%T A333218 610,616,649,652,657,664,708,712,786,788,802,808,836,840,16933,16934,
%U A333218 16937,16940,16946,16948,16965,16966,16977,16984,16994,17000,17033,17036,17041
%N A333218 Numbers k such that the k-th composition in standard order is a permutation (of an initial interval).
%C A333218 The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again.
%e A333218 The sequence of terms together with their corresponding compositions begins:
%e A333218         0: ()             593: (3,2,4,1)      16937: (5,4,2,3,1)
%e A333218         1: (1)            600: (3,2,1,4)      16940: (5,4,2,1,3)
%e A333218         5: (2,1)          610: (3,1,4,2)      16946: (5,4,1,3,2)
%e A333218         6: (1,2)          616: (3,1,2,4)      16948: (5,4,1,2,3)
%e A333218        37: (3,2,1)        649: (2,4,3,1)      16965: (5,3,4,2,1)
%e A333218        38: (3,1,2)        652: (2,4,1,3)      16966: (5,3,4,1,2)
%e A333218        41: (2,3,1)        657: (2,3,4,1)      16977: (5,3,2,4,1)
%e A333218        44: (2,1,3)        664: (2,3,1,4)      16984: (5,3,2,1,4)
%e A333218        50: (1,3,2)        708: (2,1,4,3)      16994: (5,3,1,4,2)
%e A333218        52: (1,2,3)        712: (2,1,3,4)      17000: (5,3,1,2,4)
%e A333218       549: (4,3,2,1)      786: (1,4,3,2)      17033: (5,2,4,3,1)
%e A333218       550: (4,3,1,2)      788: (1,4,2,3)      17036: (5,2,4,1,3)
%e A333218       553: (4,2,3,1)      802: (1,3,4,2)      17041: (5,2,3,4,1)
%e A333218       556: (4,2,1,3)      808: (1,3,2,4)      17048: (5,2,3,1,4)
%e A333218       562: (4,1,3,2)      836: (1,2,4,3)      17092: (5,2,1,4,3)
%e A333218       564: (4,1,2,3)      840: (1,2,3,4)      17096: (5,2,1,3,4)
%e A333218       581: (3,4,2,1)    16933: (5,4,3,2,1)    17170: (5,1,4,3,2)
%e A333218       582: (3,4,1,2)    16934: (5,4,3,1,2)    17172: (5,1,4,2,3)
%t A333218 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A333218 Select[Range[0,1000],#==0||UnsameQ@@stc[#]&&Max@@stc[#]==Length[stc[#]]&]
%Y A333218 A superset of A164894.
%Y A333218 Also a superset of A246534.
%Y A333218 Not requiring the parts to be distinct gives A333217.
%Y A333218 Cf. A000120, A000142, A048793, A066099, A070939, A114994, A225620, A233564, A272919, A333219, A333221, A333255, A333256.
%K A333218 nonn
%O A333218 1,3
%A A333218 _Gus Wiseman_, Mar 16 2020