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 A167237 Lower trim of the Wythoff fractal sequence, A003603. 3
 1, 2, 1, 3, 2, 1, 4, 5, 3, 2, 6, 1, 7, 4, 8, 5, 3, 9, 2, 10, 6, 1, 11, 7, 4, 12, 13, 8, 5, 14, 3, 15, 9, 2, 16, 10, 6, 17, 1, 18, 11, 7, 19, 4, 20, 12, 21, 13, 8, 22, 5, 23, 14, 3, 24, 15, 9, 25, 2, 26, 16, 10, 27, 6, 28, 17, 1, 29, 18, 11, 30, 7, 31, 19, 4, 32, 20, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A fractal sequence: if you delete the first occurrence of each positive integer, the remaining sequence is the original. This procedure is called upper trimming, in contrast to lower trimming, which consists of subtracting 1 from each term of the original fractal sequence and then deleting all 0's. In general, the lower trim of a fractal sequence is a fractal sequence; in particular, the lower trim of A003603 is A167237. REFERENCES Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168. LINKS FORMULA Although A167237 is closely associated with the Wythoff array (A035513) and Fibonacci numbers (A000045), it can be constructed independently. First, construct the fractal sequence of the Wythoff array inductively as described at A003603; then subtract 1 from all terms and delete all 0's. EXAMPLE The first 7 rows in the construction of A003603 are 1 1 1 2 1 3 2 1 4 3 2 5 1 6 4 3 7 2 8 5 1 9 6 4 10 3 11 7 2 12 8 5 13 Subtracting 1 and deleting 0's leaves 1 2 1 3 2 1 4 5 4 2 6 1 7 4 8 5 3 9 2 10 6 1 11 7 4 12 CROSSREFS Cf. A003603, A019586, A035513. Sequence in context: A183917 A181971 A104741 * A277813 A200154 A208825 Adjacent sequences:  A167234 A167235 A167236 * A167238 A167239 A167240 KEYWORD nonn AUTHOR Clark Kimberling, Oct 31 2009 STATUS approved

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Last modified December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)