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 A350355 Numbers k such that the k-th composition in standard order is up/down. 6
 0, 1, 2, 4, 6, 8, 12, 13, 16, 20, 24, 25, 32, 40, 41, 48, 49, 50, 54, 64, 72, 80, 81, 82, 96, 97, 98, 102, 108, 109, 128, 144, 145, 160, 161, 162, 166, 192, 193, 194, 196, 198, 204, 205, 216, 217, 256, 272, 288, 289, 290, 320, 321, 322, 324, 326, 332, 333, 384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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. A composition is up/down if it is alternately strictly increasing and strictly decreasing, starting with an increase. For example, the partition (3,2,2,2,1) has no up/down permutations, even though it does have the anti-run permutation (2,3,2,1,2). LINKS FORMULA A345167 = A350355 \/ A350356. EXAMPLE The terms together with the corresponding compositions begin: 0: () 1: (1) 2: (2) 4: (3) 6: (1,2) 8: (4) 12: (1,3) 13: (1,2,1) 16: (5) 20: (2,3) 24: (1,4) 25: (1,3,1) 32: (6) 40: (2,4) 41: (2,3,1) 48: (1,5) 49: (1,4,1) 50: (1,3,2) 54: (1,2,1,2) MATHEMATICA updoQ[y_]:=And@@Table[If[EvenQ[m], y[[m]]>y[[m+1]], y[[m]]

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Last modified February 6 04:17 EST 2023. Contains 360095 sequences. (Running on oeis4.)