A065168 Permutation t->t-1 of Z, folded to N.

3, 1, 5, 2, 7, 4, 9, 6, 11, 8, 13, 10, 15, 12, 17, 14, 19, 16, 21, 18, 23, 20, 25, 22, 27, 24, 29, 26, 31, 28, 33, 30, 35, 32, 37, 34, 39, 36, 41, 38, 43, 40, 45, 42, 47, 44, 49, 46, 51, 48, 53, 50, 55, 52, 57, 54, 59, 56, 61, 58, 63, 60, 65, 62, 67, 64, 69, 66, 71, 68, 73, 70

Offset: 1

Author

Antti Karttunen, Oct 19 2001

Keywords

• nonn
• easy

Comments

This permutation consists of just one cycle, which is infinite.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Inverse permutation to A065164.

Obtained by composing permutations A065190 and A014681.

Programs

Maple

a:= n-> n-2*(-1)^n +`if`(n=2, 1, 0):
seq(a(n), n=1..80); # Alois P. Heinz, Mar 07 2012

Mathematica

Join[{3, 1}, LinearRecurrence[{1, 1, -1}, {5, 2, 7}, 100]] (* Jean-François Alcover, Feb 28 2016 *)

Formula

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).

G.f.: x*(3-2*x+x^4+x^2-x^3) / ((x+1)*(x-1)^2). - Alois P. Heinz, Mar 07 2012

Sum_{n>=1} (-1)^n/a(n) = 2 - log(2). - Amiram Eldar, Aug 08 2023