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Search: id:A137457
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| A137457 |
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Consider a row of standard dice as a counter. This sequence enumerates the number of changes (one face rotated over an edge to an adjacent face) from n-1 to n. |
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+0
1
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| 0, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 5, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 5, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Most counters 'zero' out at '0' but the dice 'zero' out at '1' which is the initial state. So to increment 1 -> 2 requires 1 move, 2 -> 3 requires 1 move, 3 -> 4 requires 2 moves, 4 -> 5 requires 1 move, 5 -> 6 requires 1 move and 6 -> 0 requires 2 moves.
First occurrence of k (A026532): 1, 3, 6, 18, 36, 108, 216, 648, 1296, 3888, ....
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Dice.
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MATHEMATICA
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f[n_] := Block[{a = IntegerDigits[n - 1, 6] + 1, b = IntegerDigits[n, 6] + 1, c}, If[Length@b > Length@a, a = Prepend[a, 1]]; c = Transpose[{a, b}] /. {{d_, d_} -> 0, {1, 2} -> 1, {2, 3} -> 1, {3, 4} -> 2, {4, 5} -> 1, {5, 6} -> 1, {6, 1} -> 2}; Plus @@ c]; Array[f, 105]
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CROSSREFS
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Cf. A057436, A060852, A026532, A133794.
Sequence in context: A160182 A098824 A124032 this_sequence A007862 A055169 A010783
Adjacent sequences: A137454 A137455 A137456 this_sequence A137458 A137459 A137460
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 18 2008
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