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A244817
The hexagonal spiral of Champernowne, read along the 150-degree ray.
11
1, 7, 4, 3, 5, 0, 8, 9, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 1, 9, 1, 1, 2, 6, 3, 3, 7, 7, 5, 6, 6, 2, 8, 8, 9, 1, 1, 1, 6, 4, 4, 5, 7, 1, 7, 8, 2, 2, 1, 2, 1, 7, 4, 5, 4, 6, 9, 0, 1, 9, 3, 4, 2, 6, 7, 8, 7, 7, 2, 3, 6, 2, 7, 8, 9, 1, 2, 4, 6, 4, 8, 9, 7, 1, 4, 5, 2, 2, 0, 1, 1, 7
OFFSET
1,2
FORMULA
(3n^2 - 3n + 1)th almost natural number (A033307), Also see formula section of A056105.
EXAMPLE
see A244807 example section for its diagram.
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_] := 3n^2 - 3n + 1 (* see formula section of A244807 *); Array[ almostNatural[ f@#, 10] &, 105]
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jul 06 2014
STATUS
approved