A333363 Horizontal visibility sequence at the onset of chaos in the 3-period cascade.
3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 11, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 13, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 11, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 15
Offset: 1
Examples
From _Omar E. Pol_, Mar 16 2020: (Start) Written as a table with six columns read by rows: 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 9; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 11; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 9; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 13; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 9; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 11; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 9; 3, 2, 5, 3, 2, 7; 3, 2, 5, 3, 2, 15; (End)
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Juan C. Nuño and Francisco J. Muñoz, Universal visibility patterns of unimodal maps, arXiv:2002.10423 [nlin.CD], 2020.
- Juan C. Nuño and Francisco J. Muñoz, Universal visibility patterns of unimodal maps, Chaos, 30, 063105 (2020).
- Juan Carlos Nuño and Francisco J. Muñoz, On the ubiquity of the ruler sequence, arXiv:2009.14629 [math.HO], 2020.
- Juan Carlos Nuño and Francisco J. Muñoz, The Ruler Sequence Revisited: A Dynamic Perspective, Mathematics (2024) Vol. 12, No. 5, 742.
Programs
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Mathematica
L[n_] := L[n] = Block[{s = {3, 2, 2*n+3}}, Do[s = Join[L[i], s], {i, n-1}]; s]; L[6] (* Giovanni Resta, Mar 16 2020 *) -
R
visibsuc3 <- function(n){ suc <- c(3,2, 2*(n+1)+1) if(n>1){ for(i in 1:(n-1)){ suc <- c(visibsuc3(i), suc) } } return(suc) }
Formula
Conjectured: a(n) = 2*A007814(n/3) + 5 if 3|n and a(n) = 4 - (n mod 3) otherwise. - Giovanni Resta, Mar 16 2020
Comments