|
|
A335933
|
|
A fractal function, related to ruler functions. a(1) = 0; otherwise for m >= 0, a(3m) = 1, a(3m-1) = a(2m-1) + sign(a(2m-1)), a(3m+1) = a(2m+1) + sign(a(2m+1)).
|
|
3
|
|
|
1, 0, 0, 1, 2, 2, 1, 3, 3, 1, 4, 4, 1, 2, 2, 1, 5, 5, 1, 3, 3, 1, 2, 2, 1, 6, 6, 1, 4, 4, 1, 2, 2, 1, 3, 3, 1, 7, 7, 1, 2, 2, 1, 5, 5, 1, 3, 3, 1, 2, 2, 1, 4, 4, 1, 8, 8, 1, 2, 2, 1, 3, 3, 1, 6, 6, 1, 2, 2, 1, 4, 4, 1, 3, 3, 1, 2, 2, 1, 5, 5, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
We choose a form for the definition that shows clearly its relationship to A307744.
The odd bisection is essentially A087088.
If we add a(-1) = 0 to the definition and allow negative m (and therefore n), we get a symmetric function, that is a(n) = a(-n).
For k >= 1 numbers 1..k occur with the same periodic and mirror symmetries as in A307744 and in ruler function A051064. In A051064, k occurs 3 times more frequently than k+1. Here, and in A307744, k occurs 3/2 times more frequently than k+1, precisely 2^(k-1) times in every 3^k terms.
|
|
LINKS
|
|
|
PROG
|
(PARI) a(n) = if (n==1, 0, if ((n%3) == 0, 1, if ((n%3)==1, my(k=(n-1)/3, aa = a(2*k+1)); aa+sign(aa), my(k=(n+1)/3, aa = a(2*k-1)); aa+sign(aa)))); \\ Michel Marcus, Jul 03 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|