A137457 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.

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

Offset

0,4

Comments

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, ....

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Dice.

Wikipedia, Dice.

Mathematica

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]

Crossrefs

Cf. A057436, A060852, A026532, A133794.

Sequence in context: A181651 A124032 A254046 * A275699 A305633 A214123

Adjacent sequences: A137454 A137455 A137456 * A137458 A137459 A137460

Keyword

nonn

Author

Robert G. Wilson v, Apr 18 2008

Status

approved