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

1,2

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

Table of n, a(n) for n=1..72.

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

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);

Crossrefs

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

Sequence in context: A040035 A065272 A070394 * A065284 A050088 A163864

Adjacent sequences: A065171 A065172 A065173 * A065175 A065176 A065177

Keyword

nonn

Author

Antti Karttunen, Oct 19 2001

Status

approved