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 A162598 Ordinal transform of A265332. 7
 1, 1, 2, 1, 3, 4, 2, 1, 5, 6, 7, 3, 8, 4, 2, 1, 9, 10, 11, 12, 5, 13, 14, 6, 15, 7, 3, 16, 8, 4, 2, 1, 17, 18, 19, 20, 21, 9, 22, 23, 24, 10, 25, 26, 11, 27, 12, 5, 28, 29, 13, 30, 14, 6, 31, 15, 7, 3, 32, 16, 8, 4, 2, 1, 33, 34, 35, 36, 37, 38, 17, 39, 40, 41, 42, 18, 43, 44, 45, 19, 46, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This is a fractal sequence. It appears that each group of 2^k terms starts with 1 and ends with the remaining powers of two from 2^k down to 2^1. From Antti Karttunen, Jan 09-12 2016: (Start) This is ordinal transform of A265332, which is modified A051135 (with a(1) = 1, instead of 2). -  after Franklin T. Adams-Watters' original definition for this sequence. A000079 (powers of 2) indeed gives the positions of ones in this sequence. This follows from the properties (3) and (4) of A004001 given on page 227 of Kubo & Vakil paper (page 3 of PDF), which together also imply the pattern observed above, more clearly represented as: a(2) = 1. a(3..4) = 2, 1. a(6..8) = 4, 2, 1. a(13..16) = 8, 4, 2, 1. a(28..31) = 16, 8, 4, 2, 1. etc. (End) LINKS Antti Karttunen, Table of n, a(n) for n = 1..8192 T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252. FORMULA Let b(1) = 1, b(n) = A051135(n) for n > 1. Then a(n) is the number of b(k) that equal b(n) for 1 <= k <= n: sum( 1, 1<=k<=n and a(k)=a(n) ). If A265332(n) = 1, then a(n) = A004001(n), otherwise a(n) = a(A080677(n)-1) = a(n - A004001(n)). - Antti Karttunen, Jan 09 2016 PROG (Scheme, with memoization-macro definec) (definec (A162598 n) (if (= 1 (A265332 n)) (A004001 n) (A162598 (- (A080677 n) 1)))) ;; Antti Karttunen, Jan 09 2016 CROSSREFS Cf. A004001, A051135, A080677, A087686. Row index of A265901, column index of A265903. Cf. A265332 (corresponding other index). Cf. A000079 (positions of ones). Cf. A000225 (from the term 3 onward the positions of 2's). Cf. A000325 (from its third term 5 onward the positions of 3's, which occur always as the last term before the next descending subsequence of powers of two). Sequence in context: A123390 A306806 A306805 * A088208 A081878 A088606 Adjacent sequences:  A162595 A162596 A162597 * A162599 A162600 A162601 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Jul 07 2009 EXTENSIONS Name amended by Antti Karttunen, Jan 09 2016 STATUS approved

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Last modified May 5 19:23 EDT 2021. Contains 343573 sequences. (Running on oeis4.)