A334751 - OEIS

%I #15 May 11 2020 15:15:59

%S 8,9,2,1,6,7,22,23,24,25,10,11,12,3,4,5,18,19,20,21,44,45,46,47,48,49,

%T 26,27,28,29,30,13,14,15,16,17,38,39,40,41,42,43,74,75,76,77,78,79,80,

%U 81,50,51,52,53,54,55,56,31,32,33,34,35,36,37,66,67,68,69

%N a(n) is the number immediately above n in a clockwise square spiral of the positive integers with the first step to the right.

%C Equivalently the number immediately below n in a counterclockwise spiral of the positive integers with the first step to the right.

%C This is a permutation of the positive integers. A334752 is the inverse permutation.

%H Peter Kagey, <a href="/A334751/b334751.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e For n = 1, a(1) = 8 because 8 is immediately above one in the clockwise square spiral with first step to the right:

%e   21--22--23--24--25--26

%e   |                    |

%e   20  7---8---9---10  27

%e   |   |            |   |

%e   19  6   1---2   11  28

%e   |   |       |    |   |

%e   18  5---4---3   12  29

%e   |                |   |

%e   17--16--15--14--13  30

%e                        |

%e   36--35--34--33--32--31

%Y Cf. A068225 (right), A068226 (left), A334752 (below).

%Y Cf. A174344 (x-coordinate), A268038 (y-coordinate).

%K nonn

%O 1,1

%A _Peter Kagey_, May 10 2020