cp's OEIS Frontend

A090930 Permutation of natural numbers arising from a square spiral.

%I A090930 #18 Jul 05 2022 11:14:25
%S A090930 1,2,9,8,7,6,5,4,3,12,11,10,25,24,23,22,21,20,19,18,17,16,15,14,13,30,
%T A090930 29,28,27,26,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,
%U A090930 56,55,54,53,52,51,50,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66
%N A090930 Permutation of natural numbers arising from a square spiral.
%C A090930 Write out the natural numbers in a square counterclockwise spiral:
%C A090930 .
%C A090930   17--16--15--14--13
%C A090930    |               |
%C A090930   18   5---4---3  12
%C A090930    |   |       |   |
%C A090930   19   6   1---2  11
%C A090930    |   |           |
%C A090930   20   7---8---9--10
%C A090930    |
%C A090930   21--22--23--24--25
%C A090930 .
%C A090930 Now read off the numbers in a clockwise spiral: 1 -> 2 -> 9 -> 8 -> 7 -> 6 -> 5 -> 4 -> 3 -> 12 -> etc.
%H A090930 Eric M. Schmidt, <a href="/A090930/b090930.txt">Table of n, a(n) for n = 1..1000</a>
%t A090930 With[{x = Floor[(Floor[Sqrt[n-1]] +1)/2]}, Table[8*x^2 -n +2 +x*If[n <= 4*x^2 -2*x, -6, 2], {n, 1, 75}]] (* _G. C. Greubel_, Feb 05 2019 *)
%o A090930 (Sage)
%o A090930 def a(n):
%o A090930     x = (isqrt(n-1)+1)//2
%o A090930     return 8*x^2 + (-6 if n <= 4*x^2 - 2*x else 2)*x + 2 - n
%o A090930 [a(n) for n in (1..75)]
%o A090930 # _Eric M. Schmidt_, May 18 2016
%o A090930 (PARI) {s(n) = ((sqrtint(n-1)+1)/2)\1};
%o A090930 for(n=1,75, print1(8*s(n)^2 -n +2 +s(n)*if(n <= 2*s(n)*(2*s(n)-1), -6, 2), ", ")) \\ _G. C. Greubel_, Feb 05 2019
%Y A090930 Cf. A020703, A090861, A090915, A090925, A090928, A090929.
%K A090930 easy,nonn
%O A090930 1,2
%A A090930 _Felix Tubiana_, Feb 26 2004
%E A090930 Offset corrected by _Eric M. Schmidt_, May 18 2016