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 A074078 Number of steps to reach an integer starting with s = n/3 and iterating the map x -> s*ceiling(x). 8
 0, 2, 4, 0, 1, 1, 0, 13, 2, 0, 3, 2, 0, 1, 1, 0, 2, 4, 0, 8, 5, 0, 1, 1, 0, 7, 9, 0, 2, 7, 0, 1, 1, 0, 3, 2, 0, 6, 2, 0, 1, 1, 0, 2, 3, 0, 10, 3, 0, 1, 1, 0, 3, 3, 0, 2, 3, 0, 1, 1, 0, 5, 2, 0, 5, 2, 0, 1, 1, 0, 2, 10, 0, 3, 7, 0, 1, 1, 0, 8, 4, 0, 2, 6, 0, 1, 1, 0, 5, 2, 0, 3, 2, 0, 1, 1, 0, 2, 5, 0, 4, 6, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS EXAMPLE s = 5/3 -> 10/3 -> 20/3 -> 35/3 -> 20, so a(5) = 4. MAPLE f := proc(b1, b2) local c1, c2, t1, t2, t3, t4, i; c1 := numer(b1/b2); c2 := denom(b1/b2); i := 0; while c2 <> 1 do i := i+1; t1 := ceil(c1/c2); t2 := b1*t1; t3 := t2/b2; c1 := numer(t3); c2 := denom(t3); od: RETURN(i); end; [seq(f(n, 3), n=4..120)]; MATHEMATICA ce[n_] := Length[NestWhileList[(n/3)*Ceiling[#] &, n/3, ! IntegerQ[#] &]] - 1; Table[ce[n], {n, 3, 108}] (* Jayanta Basu, Jul 30 2013 *) CROSSREFS Cf. A072340, A074090, A074091, A074096. Records are in A074097, A074098. First integer reached: A081852. Sequence in context: A327005 A300858 A276995 * A309635 A130659 A083741 Adjacent sequences:  A074075 A074076 A074077 * A074079 A074080 A074081 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 16 2002 STATUS approved

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Last modified September 18 20:10 EDT 2021. Contains 347534 sequences. (Running on oeis4.)