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

1,1

Comments

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

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Index entries for sequences that are permutations of the natural numbers.

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

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 *)

Crossrefs

Inverse permutation to A065164.

Obtained by composing permutations A065190 and A014681.

Sequence in context: A331381 A174239 A066249 * A318581 A065277 A249139

Adjacent sequences: A065165 A065166 A065167 * A065169 A065170 A065171

Keyword

nonn,easy

Author

Antti Karttunen, Oct 19 2001

Status

approved