OFFSET
1,2
COMMENTS
Write out the natural numbers in a square counterclockwise spiral:
.
17--16--15--14--13
| |
18 5---4---3 12
| | | |
19 6 1---2 11
| | |
20 7---8---9--10
|
21--22--23--24--25
.
Now read off the numbers in a counterclockwise spiral: 1 -> 8 -> 9 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 22 -> etc.
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..1000
MATHEMATICA
With[{x = Floor[(Floor[Sqrt[n-1]] +1)/2]}, Table[If[n +6*x <= (2*x+1)^2, n +6*x, n -2*x], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)
PROG
(Sage)
def a(n):
x = (isqrt(n-1)+1)//2
return n + 6*x if n + 6*x <= (2*x+1)^2 else n - 2*x
[a(n) for n in (1..75)]
# Eric M. Schmidt, May 18 2016
(PARI) {s(n) = ((sqrtint(n-1)+1)/2)\1};
for(n=1, 75, print1(if(n+6*s(n) <= (2*s(n)+1)^2, n +6*s(n), n - 2*s(n)), ", ")) \\ G. C. Greubel, Feb 05 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Felix Tubiana, Feb 26 2004
EXTENSIONS
Offset corrected by Eric M. Schmidt, May 18 2016
STATUS
approved