1,1

Corresponds to simple periodic asynchronic site swap pattern ...111111... (tossing one ball from hand to hand forever).

This permutation consists of a single infinite cycle.

This is, starting at a(2) = 4, the same as the "increasing oscillating sequence" shown in Proposition 3.1, p.7, and plotted in the right of figure 1, of Vatter. The same paper, p.4, cites Comtet and uses without giving the A-number of A003319. Abstract: We prove that there are permutation classes (hereditary properties of permutations) of every growth rate (Stanley-Wilf limit) at least lambda = approx 2.48187, the unique real root of x^5-2x^4-2x^2-2x-1, thereby establishing a conjecture of Albert and Linton. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 18 2008

Joe Buhler and Ron Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.

Index entries for sequences that are permutations of the natural numbers

Vincent Vatter, Permutation classes of every growth rate (a.k.a. Stanley-Wilf limit) above 2.48187.., Jul 17, 2008.

Let f: Z -> N be given by f(z) = 2z if z>0 else 2|z|+1, with inverse g(z) = z/2 if z even else (1-z)/2. Then a(n) = f(g(n)+1).

a(n) = n + 2*(-1^n) for n > 1. - Frank Ellermann, Feb 12, 2002

ss1 := [seq(PerSS(n, 1), n=1..120)]; PerSS := (n, c) -> Z2N(N2Z(n)+c);

N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1), 1, 0);

Row 1 of A065167. Obtained by composing permutations A014681 and A065190. Inverse permutation: A065168.

Adjacent sequences: A065161 A065162 A065163 this_sequence A065165 A065166 A065167

Sequence in context: A096907 A081879 A066248 this_sequence A138124 A128860 A019680

nonn

Antti Karttunen Oct 19 2001