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 A110963 Fractalization of Kimberling's paraphrases sequence beginning with 1. 5
 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 4, 1, 1, 1, 5, 3, 3, 2, 6, 2, 2, 1, 7, 4, 4, 1, 8, 1, 1, 1, 9, 5, 5, 3, 10, 3, 3, 2, 11, 6, 6, 2, 12, 2, 2, 1, 13, 7, 7, 4, 14, 4, 4, 1, 15, 8, 8, 1, 16, 1, 1, 1, 17, 9, 9, 5, 18, 5, 5, 3, 19, 10, 10, 3, 20, 3, 3, 2, 21, 11, 11, 6, 22, 6, 6, 2, 23, 12, 12, 2, 24, 2, 2, 1, 25, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Self-descriptive sequence: terms at even indices are the sequence itself, terms at odd indices (the skeleton of this sequence) are the terms of Kimberling's paraphrases sequence (A003602) beginning with 1. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 Clark Kimberling, Fractal sequences. FORMULA For even n, a(n) = a(n/2), for odd n, a(n) = A003602((1+n)/2). - Antti Karttunen, Apr 03 2022 For n >= 0, (Start) a(4n+2) = a(4n+3) = A003602(1+n). a(8n+1) = A005408(n) = 2*n + 1. a(4n+1) = a(8n+2) = a(8n+3) = 1+n. a(n) = A110962(n-1) + 1. (End) a(n) = A353367(4*n). - Antti Karttunen, Apr 20 2022 PROG (PARI) A003602(n) = (1+(n>>valuation(n, 2)))/2; A110963(n) = if(n%2, A003602((1+n)/2), A110963(n/2)); \\ Antti Karttunen, Apr 03 2022 CROSSREFS One more than A110962 (but note the different starting offsets). Cf. A000265, A003602, A005408, A110812, A110779, A110766, A351565 [= 2*a(n) - 1]. Cf. A353366 (Dirichlet inverse), A353367 (sum with it). Sequence in context: A288003 A304382 A304717 * A292622 A292869 A106348 Adjacent sequences: A110960 A110961 A110962 * A110964 A110965 A110966 KEYWORD base,easy,nonn AUTHOR Alexandre Wajnberg, Sep 26 2005 EXTENSIONS Entry edited, starting offset corrected (from 0 to 1), and the offsets in formulas changed accordingly, and more terms added by Antti Karttunen, Apr 03 2022 STATUS approved

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Last modified February 7 10:10 EST 2023. Contains 360115 sequences. (Running on oeis4.)