login

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”).

A105500
Trajectory of 1 under the morphism 1->{1,2}, 2->{3,2}, 3->{3,4}, 4->{1,4}.
5
1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1
OFFSET
0,2
COMMENTS
Harter-Heighway dragon when interpreting 1, 2, 3, and 4 respectively as unit edge to right, up, left, and down. - Joerg Arndt, Jun 03 2021
The characteristic polynomial of the transition matrix is x^4-4*x^3+6*x^2-4*x = x*(x-2)*(x^2 - 2*x + 2).
LINKS
F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104; page 89, section 4.5.
FORMULA
a(n) = A246960(n) + 1. - Joerg Arndt, Jun 03 2021
MATHEMATICA
Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2}, 2 -> {3, 2}, 3 -> {3, 4}, 4 -> {1, 4}} &], {1}, 7]]
PROG
(Python)
def A105500(n): return ((n^(n>>1)).bit_count()&3)+1 # Chai Wah Wu, Jul 13 2024
CROSSREFS
Cf. A246960 (as 0..3).
Indices of terms 1..4: A043724, A043725, A043726, A043727.
Sequence in context: A106383 A175794 A324389 * A288569 A088748 A323235
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 02 2005
STATUS
approved