Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Mar 25 2021 19:02:54
%S 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,
%T 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,
%U 1,2,4,5,1,2,1,3,1,5,4,3,1,2,1,3,1,2,4
%N 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.
%C 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
%D Andreas M. Hinz, The Tower of Hanoi, in Algebras and combinatorics (Hong Kong, 1997), 277-289, Springer, Singapore, 1999.
%H Andreas M. Hinz, <a href="http://dx.doi.org/10.5169/seals-87878">Squarefree Tower of Hanoi sequences</a>, Enseign. Math. (2) 42(1996), 257-264.
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%Y Cf. A101608.
%K nonn
%O 1,2
%A _Andreas M. Hinz_, Dec 11 1999
%E More terms from _Sean A. Irvine_, Mar 24 2021