A074305 a(3m) = 2m, a(3m+1) = 4m+3, a(3m+2) = 4m+1.

0, 3, 1, 2, 7, 5, 4, 11, 9, 6, 15, 13, 8, 19, 17, 10, 23, 21, 12, 27, 25, 14, 31, 29, 16, 35, 33, 18, 39, 37, 20, 43, 41, 22, 47, 45, 24, 51, 49, 26, 55, 53, 28, 59, 57, 30, 63, 61, 32, 67, 65, 34, 71, 69, 36, 75, 73, 38, 79, 77, 40, 83, 81, 42, 87, 85, 44, 91, 89, 46, 95, 93

Offset

0,2

Comments

A permutation of the nonnegative integers.

Links

Table of n, a(n) for n=0..71.

G. Venturini, Iterates of number-theoretic functions with periodic rational coefficients (Generalization of the 3x+1 problem), Stud. Appl. Math., 86 (1992), 185-218.

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

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

Formula

G.f.: x*(x^2-x+1)*(3x^2+4x+3)/(x^3-1)^2. - Ralf Stephan, Mar 19 2003

Sum_{n>=1} (-1)^n/a(n) = (sqrt(2)*arcsinh(1) - log(2))/2. - Amiram Eldar, Nov 28 2023

Mathematica

a[n_] := a[n] = If[n <= 5, {0, 3, 1, 2, 7, 5}[[n+1]], 2 a[n-3] - a[n-6]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 22 2023 *)

Prog

(PARI) a(m) = if(m%3==0, m/3*2, if(m%3==1, (m-1)/3*4+3, (m-2)/3*4+1)); \\ C. Ronaldo

Crossrefs

Cf. A074306, A074307, A074308.

Sequence in context: A308001 A191862 A266055 * A151855 A186366 A135338

Adjacent sequences: A074302 A074303 A074304 * A074306 A074307 A074308

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 23 2002

Extensions

More terms from Ralf Stephan, Mar 19 2003

Status

approved