A074078 Number of steps to reach an integer starting with s = n/3 and iterating the map x -> s*ceiling(x).

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

Offset

3,2

Links

Table of n, a(n) for n=3..108.

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