A084491 Permutation of Z, obtained by reflecting the juggling sequence A084501 from positive to negative numbers (with zero thrown at beat 0), folded to N with functions N2Z and Z2N.

1, 8, 2, 10, 4, 12, 6, 16, 3, 14, 5, 18, 7, 20, 11, 22, 9, 24, 13, 28, 15, 26, 17, 32, 19, 30, 23, 34, 21, 38, 27, 40, 25, 36, 29, 46, 35, 42, 31, 44, 33, 52, 39, 50, 41, 48, 37, 54, 47, 56, 45, 58, 43, 60, 49, 62, 51, 64, 53, 68, 55, 66, 57, 70, 59, 74, 63, 72, 61, 76, 65, 78

Offset: 1

Author

Antti Karttunen, Jun 02 2003

Keywords

• nonn

Comments

This permutation consists of three infinite cycles + infinite number of fixed points.

Links

• A. Karttunen, Scheme-program for computing this sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A084492. Cf. also A084490, A084455, A084461, A084495, A084499, A065166.

Programs

Maple

[seq(Z2N(A084491_Z2Z(N2Z(n))),n=1..45)];
N2Z := n -> ((-1)^n)*floor(n/2);
Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);
A084491_Z2Z := z -> z+`if`((z > 0), A084501(z),`if`((z >= -3),2*(-z), A084501(A084490((-z)-3))));