%I #16 Aug 12 2018 21:26:49

%S 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,

%T 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,

%U 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

%N 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.

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

%H Andrey Zabolotskiy, <a href="/A033952/b033952.txt">Table of n, a(n) for n = 1..10000</a>

%e The spiral begins

%e .

%e 3---1---4---1---5

%e | |

%e 1 5---6---7 1

%e | | | |

%e 2 4 1 8 6

%e | | | | |

%e 1 3---2 9 1

%e | | |

%e 1---1---0---1 7

%e .

%t 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]]];

%t f[n_] := 4n^2 - 5n + 2; Array[ almostNatural[ f@#, 10] &, 105] (* _Robert G. Wilson v_, Aug 08 2014 *)

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

%K nonn,base,easy,nice

%O 1,2

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

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

%E Edited by _Charles R Greathouse IV_, Nov 01 2009