A065174 Permutation of Z, folded to N, corresponding to the site swap pattern ...242824202428242... (A065176).

1, 6, 2, 12, 4, 10, 3, 24, 8, 14, 7, 20, 5, 18, 11, 48, 16, 22, 15, 28, 13, 26, 19, 40, 9, 30, 23, 36, 21, 34, 27, 96, 32, 38, 31, 44, 29, 42, 35, 56, 25, 46, 39, 52, 37, 50, 43, 80, 17, 54, 47, 60, 45, 58, 51, 72, 41, 62, 55, 68, 53, 66, 59, 192, 64, 70, 63, 76, 61, 74, 67, 88

Offset: 1

Author

Antti Karttunen, Oct 19 2001

Keywords

• nonn

Comments

This permutation corresponds to the site swap pattern shown in the figure 7 of Buhler and Graham paper and consists of one fixed point (at 0, mapped here to 1) and infinite number of infinite cycles.

Links

• Joe Buhler and R. L. 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

Crossrefs

Inverse permutation: A065175. A065176 gives the deltas p(t)-t, i.e. the associated site swap sequence. Cf. also A065167, A065171.

Programs

Maple

[seq(Z2N(N2Z(n)+TZ2(abs(N2Z(n)))), n=1..120)]; TZ2 := proc(xx) local x,s; s := 1; x := xx; if(0 = x) then RETURN(0); fi; while(0 = (x mod 2)) do x := floor(x/2); s := s+1; od; RETURN(2^s); end;
N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);