A065168 - OEIS

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

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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