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 A333217 Numbers k such that the k-th composition in standard order covers an initial interval of positive integers. 111
 0, 1, 3, 5, 6, 7, 11, 13, 14, 15, 21, 22, 23, 26, 27, 29, 30, 31, 37, 38, 41, 43, 44, 45, 46, 47, 50, 52, 53, 54, 55, 58, 59, 61, 62, 63, 75, 77, 78, 83, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 101, 102, 105, 106, 107, 108, 109, 110, 111, 114, 116, 117, 118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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. LINKS EXAMPLE The sequence of terms together with the corresponding compositions begins:     0: ()              37: (3,2,1)           75: (3,2,1,1)     1: (1)             38: (3,1,2)           77: (3,1,2,1)     3: (1,1)           41: (2,3,1)           78: (3,1,1,2)     5: (2,1)           43: (2,2,1,1)         83: (2,3,1,1)     6: (1,2)           44: (2,1,3)           85: (2,2,2,1)     7: (1,1,1)         45: (2,1,2,1)         86: (2,2,1,2)    11: (2,1,1)         46: (2,1,1,2)         87: (2,2,1,1,1)    13: (1,2,1)         47: (2,1,1,1,1)       89: (2,1,3,1)    14: (1,1,2)         50: (1,3,2)           90: (2,1,2,2)    15: (1,1,1,1)       52: (1,2,3)           91: (2,1,2,1,1)    21: (2,2,1)         53: (1,2,2,1)         92: (2,1,1,3)    22: (2,1,2)         54: (1,2,1,2)         93: (2,1,1,2,1)    23: (2,1,1,1)       55: (1,2,1,1,1)       94: (2,1,1,1,2)    26: (1,2,2)         58: (1,1,2,2)         95: (2,1,1,1,1,1)    27: (1,2,1,1)       59: (1,1,2,1,1)      101: (1,3,2,1)    29: (1,1,2,1)       61: (1,1,1,2,1)      102: (1,3,1,2)    30: (1,1,1,2)       62: (1,1,1,1,2)      105: (1,2,3,1)    31: (1,1,1,1,1)     63: (1,1,1,1,1,1)    106: (1,2,2,2) MATHEMATICA normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]]; stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse; Select[Range[0, 100], normQ[stc[#]]&] CROSSREFS Sequences covering an initial interval are counted by A000670. Composition in standard order are A066099. The case of strictly increasing initial intervals is A164894. The case of strictly decreasing initial intervals is A246534. The case of permutations is A333218. The weakly increasing version is A333379. The weakly decreasing version is A333380. Cf. A000120, A029931, A048793, A070939, A225620, A228351, A233564, A272919, A333219, A333220. Sequence in context: A328952 A072600 A047582 * A342438 A301975 A015814 Adjacent sequences:  A333214 A333215 A333216 * A333218 A333219 A333220 KEYWORD nonn AUTHOR Gus Wiseman, Mar 15 2020 STATUS approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)