A090925 Permutation of natural numbers arising from a square spiral.

1, 4, 5, 6, 7, 8, 9, 2, 3, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 10, 11, 12, 13, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80

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 square counterclockwise spiral: 1 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> 2 -> 3 -> 14 -> 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+2*x <= (2*x+1)^2, n +2*x, n-6*x], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

Prog

(Sage)
def a(n):
    x = (isqrt(n-1)+1)//2
    return n + 2*x if n + 2*x <= (2*x+1)^2 else n - 6*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+2*s(n) <= (2*s(n)+1)^2, n +2*s(n), n - 6*s(n)), ", ")) \\ G. C. Greubel, Feb 05 2019

Crossrefs

Cf. A020703, A090861, A090915, A090928, A090929, A090930.

Sequence in context: A239440 A248355 A178053 * A143836 A168094 A367063

Adjacent sequences: A090922 A090923 A090924 * A090926 A090927 A090928

Keyword

easy,nonn

Author

Felix Tubiana, Feb 26 2004

Extensions

Offset corrected by Eric M. Schmidt, May 18 2016

Status

approved