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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Sep 28 2003
STATUS
approved

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Last modified April 20 09:57 EDT 2024. Contains 371806 sequences. (Running on oeis4.)