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The hexagonal spiral of Champernowne, read along the 210-degree ray.
11

%I #7 Mar 14 2015 00:12:48

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

%T 1,1,7,1,9,1,7,1,1,1,1,1,7,1,9,2,7,2,1,2,1,2,7,2,9,2,7,3,1,3,1,3,7,3,

%U 9,3,7,4,1,4,1,4,7,4,9,4,7,5,1,5,1,5,7,5,9,6,7,6,1,6,1,7,7,7,9,7,7,7,1,8,1

%N The hexagonal spiral of Champernowne, read along the 210-degree ray.

%F (3n^2 - 4n + 2)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_] := 3n^2 - 4n + 2 (* see formula section of A244807 *); Array[ almostNatural[ f@#, 10] &, 105]

%Y Cf. A007376, A056109, A244807, A244808, A244809, A244810, A244811, A244812, A244813, A244814, A244816, A244817, A244818.

%K nonn,easy

%O 1,2

%A _Robert G. Wilson v_, Jul 06 2014