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 A087669 The smallest index m such that b(m) is an integer, where b(0)=(2n+1)/n and b(k+1)=b(k)*floor(b(k)) for k>=0. 4
 0, 1, 3, 2, 5, 4, 5, 2, 4, 9, 19, 7, 16, 7, 8, 3, 27, 9, 5, 25, 10, 11, 32, 4, 13, 4, 17, 6, 17, 6, 78, 3, 23, 47, 13, 6, 4, 6, 27, 9, 20, 6, 4, 17, 9, 28, 106, 4, 24, 28, 37, 20, 27, 10, 12, 13, 7, 83, 108, 10, 16, 9, 6, 3, 10, 11, 15, 8, 11, 6, 156, 15, 38, 46, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It is conjectured that an integer is always reached if the initial value is >= 2. LINKS Max Alekseyev, Table of n, a(n) for n = 1..10000 J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128. MAPLE A087669 := proc(n) local b, stps ; stps := 0 ; b := (2*n+1)/n ; while not type(b, 'integer') do b := b*floor(b) ; stps := stps+1 ; od ; RETURN(stps) ; end: for n from 1 to 100 do print(n, A087669(n)) ; od ; # R. J. Mathar, Feb 12 2007 CROSSREFS The records and their indices are given by A192230 and A192229. Cf. A087670 (integer reached), A087666. Sequence in context: A292776 A061313 A259846 * A053087 A316519 A062327 Adjacent sequences:  A087666 A087667 A087668 * A087670 A087671 A087672 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 27 2003 EXTENSIONS More terms from R. J. Mathar, Feb 12 2007 Terms a(23) onward from Max Alekseyev, Jun 25 2011 STATUS approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)