A083514 Number of steps for iteration of map x -> (4/3)*ceiling(x) to reach an integer > 3n+1 when started at 3n+1, or -1 if no such integer is ever reached.

3, 2, 8, 7, 2, 3, 5, 2, 6, 3, 2, 5, 4, 2, 3, 4, 2, 4, 3, 2, 4, 9, 2, 3, 5, 2, 6, 3, 2, 5, 5, 2, 3, 6, 2, 5, 3, 2, 7, 4, 2, 3, 4, 2, 4, 3, 2, 4, 5, 2, 3, 6, 2, 5, 3, 2, 8, 8, 2, 3, 7, 2, 7, 3, 2, 6, 4, 2, 3, 4, 2, 4, 3, 2, 4, 7, 2, 3, 8, 2, 8, 3, 2, 6, 6, 2, 3, 5, 2, 8, 3, 2, 5, 4, 2, 3, 4, 2, 4, 3, 2, 4, 6, 2, 3

Offset

0,1

Comments

It is conjectured that an integer is always reached.

Also number of steps for iteration of map x -> (4/3)*floor(x) to reach an integer when started at 3n+4.

Links

Table of n, a(n) for n=0..104.

J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Formula

a(3n+1)=2.

Maple

b:= proc(n) local i; n; for i do 4/3*ceil(%);
      if %::integer then return i fi od
    end:
a:= n-> b(3*n+1):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 01 2021

Prog

(PARI) a(n)=if(n<0, 0, c=(3*n+1)*4/3; x=1; while(frac(c)>0, c=4/3*ceil(c); x++); x)
(PARI) a(n)=if(n<0, 0, c=(3*n+4)*4/3; x=1; while(frac(c)>0, c=4/3*floor(c); x++); x)

Crossrefs

Equals A085068(3n+1).

Sequence in context: A092174 A245781 A239803 * A123696 A123500 A074689

Adjacent sequences: A083511 A083512 A083513 * A083515 A083516 A083517

Keyword

nonn,easy

Author

Benoit Cloitre, Sep 28 2003

Status

approved