|
| |
|
|
A319513
|
|
The boustrophedonic Rosenberg-Strong function maps N onto N X N where N = {0, 1, 2, ...} and n -> factor(a(n)) = 2^x*3^y -> (x, y).
|
|
2
|
|
|
|
1, 3, 6, 2, 4, 12, 36, 18, 9, 27, 54, 108, 216, 72, 24, 8, 16, 48, 144, 432, 1296, 648, 324, 162, 81, 243, 486, 972, 1944, 3888, 7776, 2592, 864, 288, 96, 32, 64, 192, 576, 1728, 5184, 15552, 46656, 23328, 11664, 5832, 2916, 1458, 729, 2187, 4374, 8748, 17496
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
If (x, y) and (x', y') are adjacent points on the trajectory of the map then for the boustrophedonic Rosenberg-Strong function max(|x - x'|, |y - y'|) is always 1 whereas for the Rosenberg-Strong function this quantity can become arbitrarily large. In this sense the boustrophedonic variant is continuous in contrast to the original Rosenberg-Strong function.
|
|
|
REFERENCES
|
A. L. Rosenberg, H. R. Strong, Addressing arrays by shells, IBM Technical Disclosure Bulletin, vol 14(10), 1972, p. 3026-3028.
|
|
|
LINKS
|
|
|
|
MAPLE
|
A319513 := proc(n) local b, r, p, m;
b := floor(sqrt(n)); r := n - b^2;
p := `if`(r < b, [b, r], [2*b-r, b]);
m := `if`(p[1] > p[2], p[1], p[2]);
`if`(irem(m, 2) = 0, 2^p[1]*3^p[2], 2^p[2]*3^p[1]) end:
|
|
|
MATHEMATICA
|
a[n_] := Module[{b, r, p1, p2, m}, b = Floor[Sqrt[n]]; r = n-b^2; {p1, p2} = If[r<b, {b, r}, {2b-r, b}]; m = If[p1>p2, p1, p2]; If[EvenQ[m], 2^p1 3^p2, 2^p2 3^p1]]; Table[a[n], {n, 0, 52}] (* Jean-François Alcover, Feb 14 2019, from Maple *)
|
|
|
PROG
|
(Julia)
function bRS(n)
m = x = isqrt(n)
y = n - x^2
x <= y && ((x, y) = (2x - y, x))
isodd(m) ? (y, x) : (x, y)
end
A319513(n) = ((x, y) = bRS(n); 2^x * 3^y)
[A319513(n) for n in 0:52] |> println
|
|
|
CROSSREFS
|
See A319514 for a non-decoded variant with interleaved x and y coordinates.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
