%I #7 Mar 14 2015 00:13:56
%S 1,1,2,6,1,1,1,2,3,3,4,5,6,7,8,9,7,5,2,1,2,1,7,1,3,7,3,2,0,2,0,3,3,6,
%T 7,3,2,1,6,4,7,5,6,5,8,8,6,6,5,1,8,8,8,4,0,9,7,1,3,1,0,1,1,8,1,2,2,1,
%U 6,1,4,4,1,5,1,5,6,1,7,1,7,8,1,0,1,9,0,2,6,2,1,2,2,3,2,3,4,2,3,2,6,6,2,4,2
%N The hexagonal spiral of Champernowne, read along the 240-degree ray.
%F (12n^2 - 21n + 10)th almost natural number (A033307), Also see formula section of A056105.
%e see A244807 example section for its diagram.
%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]]]; f[n_] := 12n^2 - 21n + 10 (* see formula section of A244807 *); Array[ almostNatural[ f@#, 10] &, 105]
%Y Cf. A007376, A244805, A244807, A244808, A244809, A244810, A244811, A244812, A244813, A244815, A244816, A244817, A244818.
%K nonn,easy
%O 1,3
%A _Robert G. Wilson v_, Jul 06 2014