cp's OEIS Frontend

A090929 Permutation of natural numbers arising from a square spiral.

%I A090929 #17 Jul 05 2022 11:13:49
%S A090929 1,8,9,2,3,4,5,6,7,22,23,24,25,10,11,12,13,14,15,16,17,18,19,20,21,44,
%T A090929 45,46,47,48,49,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
%U A090929 74,75,76,77,78,79,80,81,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64
%N A090929 Permutation of natural numbers arising from a square spiral.
%C A090929 Write out the natural numbers in a square counterclockwise spiral:
%C A090929 .
%C A090929   17--16--15--14--13
%C A090929    |               |
%C A090929   18   5---4---3  12
%C A090929    |   |       |   |
%C A090929   19   6   1---2  11
%C A090929    |   |           |
%C A090929   20   7---8---9--10
%C A090929    |
%C A090929   21--22--23--24--25
%C A090929 .
%C A090929 Now read off the numbers in a counterclockwise spiral: 1 -> 8 -> 9 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 22 -> etc.
%H A090929 Eric M. Schmidt, <a href="/A090929/b090929.txt">Table of n, a(n) for n = 1..1000</a>
%t A090929 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 *)
%o A090929 (Sage)
%o A090929 def a(n):
%o A090929     x = (isqrt(n-1)+1)//2
%o A090929     return n + 6*x if n + 6*x <= (2*x+1)^2 else n - 2*x
%o A090929 [a(n) for n in (1..75)]
%o A090929 # _Eric M. Schmidt_, May 18 2016
%o A090929 (PARI) {s(n) = ((sqrtint(n-1)+1)/2)\1};
%o A090929 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
%Y A090929 Cf. A020703, A090861, A090915, A090925, A090928, A090930.
%K A090929 easy,nonn
%O A090929 1,2
%A A090929 _Felix Tubiana_, Feb 26 2004
%E A090929 Offset corrected by _Eric M. Schmidt_, May 18 2016