|
Search: id:A083514
|
|
|
| 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. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
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.
|
|
PROGRAM
|
(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: A117822 A132887 A092174 this_sequence A123696 A123500 A074689
Adjacent sequences: A083511 A083512 A083513 this_sequence A083515 A083516 A083517
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 28 2003
|
|
|
Search completed in 0.002 seconds
|
