The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#17 by Peter Luschny at Thu Mar 25 19:02:54 EDT 2021

STATUS

proposed

approved

#16 by Sean A. Irvine at Thu Mar 25 18:16:20 EDT 2021

STATUS

editing

proposed

#15 by Sean A. Irvine at Thu Mar 25 04:51:10 EDT 2021

COMMENTS

To construct a(n), consider the six consecutive terms A101608(6*n-5) through A101608(6*n+5) 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

STATUS

proposed

editing

Discussion

Thu Mar 25

04:51

Sean A. Irvine: @Kevin Yes! You are right, thanks.

#14 by Sean A. Irvine at Wed Mar 24 23:49:29 EDT 2021

STATUS

editing

proposed

Discussion

Thu Mar 25

02:55

Kevin Ryde: Are the six terms rather 6*n-5..6*n (eg. so n=1 gives 1..6).

#13 by Sean A. Irvine at Wed Mar 24 23:48:49 EDT 2021

COMMENTS

To construct a(n), consider the six consecutive terms A101608(6*n) through A101608(6*n+5) as a single string (e.g., for n=1 we have 121313, 121323, for n=2 we have 123132). Only five different strings occur, corresponding to the five letter alphabet used here. Apply the mapping 121313 121323 -> 1, 123132 -> 2, 213123 -> 3, 123123 -> 4, 213132 -> 5. - Sean A. Irvine, Mar 24 2021

#12 by Sean A. Irvine at Wed Mar 24 23:47:25 EDT 2021

DATA

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

COMMENTS

To construct a(n), consider the six consecutive terms A101608(6*n) through A101608(6*n+5) as a single string (e.g., for n=1 we have 121313, for n=2 we have 123132). Only five different strings occur, corresponding to the five letter alphabet used here. Apply the mapping 121313 -> 1, 123132 -> 2, 213123 -> 3, 123123 -> 4, 213132 -> 5. - Sean A. Irvine, Mar 24 2021

CROSSREFS

Cf. A101608.

KEYWORD

nonn,more

nonn

EXTENSIONS

More terms from Sean A. Irvine, Mar 24 2021

STATUS

approved

editing

#11 by Joerg Arndt at Sat Nov 14 01:00:42 EST 2020

STATUS

reviewed

approved

#10 by Michel Marcus at Fri Nov 13 23:52:33 EST 2020

STATUS

proposed

reviewed

#9 by Kevin Ryde at Fri Nov 13 18:17:48 EST 2020

STATUS

editing

proposed

#8 by Kevin Ryde at Fri Nov 13 18:17:07 EST 2020

REFERENCES

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

LINKS

A. 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.

<a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>

AUTHOR

Andreas M. Hinz (hinz(AT)appl-math.tu-muenchen.de)

Andreas M. Hinz, Dec 11 1999

STATUS

approved

editing