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 A357708 Numbers k such that the k-th composition in standard order has sum equal to twice its maximum part. 1
 3, 10, 11, 13, 14, 36, 37, 38, 39, 41, 44, 50, 51, 52, 57, 60, 136, 137, 138, 139, 140, 141, 142, 143, 145, 152, 162, 163, 168, 177, 184, 196, 197, 198, 199, 200, 209, 216, 226, 227, 232, 241, 248, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The k-th composition in standard order (graded reverse-lexicographic, 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. This gives a bijective correspondence between nonnegative integers and integer compositions. LINKS Table of n, a(n) for n=1..55. Gus Wiseman, Statistics, classes, and transformations of standard compositions EXAMPLE The terms and corresponding compositions begin: 3: (1,1) 10: (2,2) 11: (2,1,1) 13: (1,2,1) 14: (1,1,2) 36: (3,3) 37: (3,2,1) 38: (3,1,2) 39: (3,1,1,1) 41: (2,3,1) 44: (2,1,3) 50: (1,3,2) 51: (1,3,1,1) MATHEMATICA stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse; Select[Range[0, 1000], Max@@stc[#]==Total[stc[#]]/2&] CROSSREFS See link for sequences related to standard compositions. A066311 lists gapless numbers. A124767 counts runs in standard compositions. A333766 gives maximal part of standard compositions, minimal A333768. A356844 ranks compositions with at least one 1. Cf. A000120, A001511, A003754, A029931, A329395. Sequence in context: A114134 A167519 A372120 * A169939 A357627 A073108 Adjacent sequences: A357705 A357706 A357707 * A357709 A357710 A357711 KEYWORD nonn AUTHOR Gus Wiseman, Oct 14 2022 STATUS approved

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Last modified August 8 12:20 EDT 2024. Contains 375021 sequences. (Running on oeis4.)