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The hexagonal spiral of Champernowne, read along the 300° -degree ray.

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The hexagonal spiral of Champernowne, read along the 300° ray.

(12n^2 - 23n + 12)th almost natural number (A033307), Also see formula section of A056105.

see A244807 example section for its diagram.

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 - 23n + 12 (* see formula section of A244807 *); Array[ almostNatural[ f@#, 10] &, 105]

Cf. A007376, A244804, A244807, A244808, A244809, A244810, A244811, A244813, A244814, A244815, A244816, A244817, A244818.

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allocated for Robert G The hexagonal spiral of Champernowne, read the 300° ray. Wilson v

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

1,4

(12n^2 - 23n + 12)th almost natural number (A033307), Also see formula section of A056105.

see A244807 example section for its diagram.

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 - 23n + 12 (* see formula section of A244807 *); Array[ almostNatural[ f@#, 10] &, 105]

Cf. A007376, A244804, A244807, A244808, A244809, A244810, A244811, A244813, A244814, A244815, A244816, A244817, A244818.

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nonn,easy

Robert G. Wilson v, Jul 06 2014

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allocated for Robert G. Wilson v

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