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