A033952 Write 1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 1 at the origin and 2 at x=0, y=-1; sequence gives the numbers on the positive x-axis.

1, 8, 6, 2, 3, 6, 6, 0, 3, 1, 8, 0, 2, 7, 1, 3, 9, 3, 4, 3, 9, 6, 0, 6, 8, 9, 6, 1, 2, 4, 2, 1, 5, 9, 4, 1, 0, 7, 7, 1, 7, 8, 0, 2, 6, 3, 4, 2, 7, 1, 8, 2, 0, 2, 2, 3, 5, 6, 6, 3, 2, 4, 1, 4, 1, 5, 6, 4, 2, 9, 2, 5, 5, 6, 8, 5, 0, 6, 4, 6, 7, 9, 0, 7, 6, 6, 7, 7, 7, 6, 4, 8, 0, 9, 1, 9, 5, 5, 9, 1, 0, 4, 0, 0, 9

Offset: 1

Author

Olivier Gorin (gorin(AT)roazhon.inra.fr)

Keywords

• nonn
• base
• easy
• nice

Comments

Same as the South spoke of the Champernowne spiral (A244677).

Examples

			The spiral begins
.
  3---1---4---1---5
  |               |
  1   5---6---7   1
  |   |       |   |
  2   4   1   8   6
  |   |   |   |   |
  1   3---2   9   1
  |           |   |
  1---1---0---1   7
.
		

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 1..10000

Crossrefs

Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.

Programs

Mathematica

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]];
f[n_] := 4n^2 - 5n + 2; Array[ almostNatural[ f@#, 10] &, 105] (* Robert G. Wilson v, Aug 08 2014 *)

Extensions

More terms from Andrew J. Gacek (andrew(AT)dgi.net)

Edited by Charles R Greathouse IV, Nov 01 2009