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

0, 1, 5, 6, 37, 38, 41, 44, 50, 52, 549, 550, 553, 556, 562, 564, 581, 582, 593, 600, 610, 616, 649, 652, 657, 664, 708, 712, 786, 788, 802, 808, 836, 840, 16933, 16934, 16937, 16940, 16946, 16948, 16965, 16966, 16977, 16984, 16994, 17000, 17033, 17036, 17041

Offset: 1

Author

Gus Wiseman, Mar 16 2020

Keywords

• nonn

Comments

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.

Examples

			The sequence of terms together with their corresponding compositions begins:
        0: ()             593: (3,2,4,1)      16937: (5,4,2,3,1)
        1: (1)            600: (3,2,1,4)      16940: (5,4,2,1,3)
        5: (2,1)          610: (3,1,4,2)      16946: (5,4,1,3,2)
        6: (1,2)          616: (3,1,2,4)      16948: (5,4,1,2,3)
       37: (3,2,1)        649: (2,4,3,1)      16965: (5,3,4,2,1)
       38: (3,1,2)        652: (2,4,1,3)      16966: (5,3,4,1,2)
       41: (2,3,1)        657: (2,3,4,1)      16977: (5,3,2,4,1)
       44: (2,1,3)        664: (2,3,1,4)      16984: (5,3,2,1,4)
       50: (1,3,2)        708: (2,1,4,3)      16994: (5,3,1,4,2)
       52: (1,2,3)        712: (2,1,3,4)      17000: (5,3,1,2,4)
      549: (4,3,2,1)      786: (1,4,3,2)      17033: (5,2,4,3,1)
      550: (4,3,1,2)      788: (1,4,2,3)      17036: (5,2,4,1,3)
      553: (4,2,3,1)      802: (1,3,4,2)      17041: (5,2,3,4,1)
      556: (4,2,1,3)      808: (1,3,2,4)      17048: (5,2,3,1,4)
      562: (4,1,3,2)      836: (1,2,4,3)      17092: (5,2,1,4,3)
      564: (4,1,2,3)      840: (1,2,3,4)      17096: (5,2,1,3,4)
      581: (3,4,2,1)    16933: (5,4,3,2,1)    17170: (5,1,4,3,2)
      582: (3,4,1,2)    16934: (5,4,3,1,2)    17172: (5,1,4,2,3)
		

Crossrefs

A superset of A164894.

Also a superset of A246534.

Not requiring the parts to be distinct gives A333217.

Cf. A000120, A000142, A048793, A066099, A070939, A114994, A225620, A233564, A272919, A333219, A333221, A333255, A333256.

Programs

Mathematica

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Select[Range[0,1000],#==0||UnsameQ@@stc[#]&&Max@@stc[#]==Length[stc[#]]&]