A045898 a(n) = one of five triples of directions in n-th triple of moves in the optimal solution of the Tower of Hanoi; it is a squarefree sequence over a five-letter alphabet.

1, 2, 1, 3, 1, 2, 4, 5, 1, 2, 1, 3, 1, 5, 4, 3, 1, 2, 1, 3, 1, 2, 4, 5, 1, 2, 4, 3, 1, 5, 4, 5, 1, 2, 1, 3, 1, 2, 4, 5, 1, 2, 1, 3, 1, 5, 4, 3, 1, 2, 1, 3, 1, 5, 4, 5, 1, 2, 4, 3, 1, 5, 4, 3, 1, 2, 1, 3, 1, 2, 4, 5, 1, 2, 1, 3, 1, 5, 4, 3, 1, 2, 1, 3, 1, 2, 4

Offset

1,2

Comments

To construct a(n), consider the six consecutive terms A101608(6*n-5) through A101608(6*n) as a single string (e.g., for n=1 we have 121323, for n=2 we have 123132). Only five different strings occur, corresponding to the five letter alphabet used here. Apply the mapping 121323 -> 1, 123132 -> 2, 213123 -> 3, 123123 -> 4, 213132 -> 5. - Sean A. Irvine, Mar 24 2021

References

Andreas M. Hinz, The Tower of Hanoi, in Algebras and combinatorics (Hong Kong, 1997), 277-289, Springer, Singapore, 1999.

Links

Table of n, a(n) for n=1..87.

Andreas M. Hinz, Squarefree Tower of Hanoi sequences, Enseign. Math. (2) 42(1996), 257-264.

Index entries for sequences related to Towers of Hanoi

Crossrefs

Cf. A101608.

Sequence in context: A323420 A331296 A270656 * A303754 A257918 A257912

Adjacent sequences: A045895 A045896 A045897 * A045899 A045900 A045901

Keyword

nonn

Author

Andreas M. Hinz, Dec 11 1999

Extensions

More terms from Sean A. Irvine, Mar 24 2021

Status

approved