

A045898


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


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

To construct a(n), consider the six consecutive terms A101608(6*n5) 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), 277289, Springer, Singapore, 1999.


LINKS



CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



