A261671 If n even, a(n) = 6n+3, otherwise a(n) = n.

3, 1, 15, 3, 27, 5, 39, 7, 51, 9, 63, 11, 75, 13, 87, 15, 99, 17, 111, 19, 123, 21, 135, 23, 147, 25, 159, 27, 171, 29, 183, 31, 195, 33, 207, 35, 219, 37, 231, 39, 243, 41, 255, 43, 267, 45, 279, 47, 291, 49, 303, 51, 315, 53, 327, 55, 339, 57, 351, 59, 363

Offset: 0

Author

N. J. A. Sloane, Sep 02 2015

Keywords

• nonn
• easy

Comments

Although the OEIS indexes sequences by consecutive integers, it is better to think of this sequence as defined on the odd numbers 1,3,5,7,... and given by f(4m+1)=12m+3, f(4m+3)=2m+1, that is, subtract 1 and divide by 2 if the result is odd, otherwise multiply by 3. This arises in analyzing A109732.

It is conjectured that starting with any positive odd number d and iterating f, we always eventually reach either 1, 9, or 33 (see Comments in A135730).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A109732, A135730.

Programs

Mathematica

Table[If[EvenQ[n],6n+3,n],{n,0,60}] (* or *) LinearRecurrence[{0,2,0,-1},{3,1,15,3},70] (* Harvey P. Dale, Dec 30 2023 *)

PARI

Vec((x^3+9*x^2+x+3)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 13 2015

Formula

From Colin Barker, Sep 13 2015: (Start)

a(n) = (3+3*(-1)^n+7*n+5*(-1)^n*n)/2.

a(n) = 2*a(n-2) - a(n-4) for n>3.

G.f.: (x^3+9*x^2+x+3) / ((x-1)^2*(x+1)^2).

(End)