This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A261671 #26 Feb 22 2024 20:27:50
%S A261671 3,1,15,3,27,5,39,7,51,9,63,11,75,13,87,15,99,17,111,19,123,21,135,23,
%T A261671 147,25,159,27,171,29,183,31,195,33,207,35,219,37,231,39,243,41,255,
%U A261671 43,267,45,279,47,291,49,303,51,315,53,327,55,339,57,351,59,363
%N A261671 If n even, a(n) = 6n+3, otherwise a(n) = n.
%C A261671 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.
%C A261671 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).
%H A261671 Colin Barker, <a href="/A261671/b261671.txt">Table of n, a(n) for n = 0..1000</a>
%H A261671 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A261671 From _Colin Barker_, Sep 13 2015: (Start)
%F A261671 a(n) = (3+3*(-1)^n+7*n+5*(-1)^n*n)/2.
%F A261671 a(n) = 2*a(n-2) - a(n-4) for n>3.
%F A261671 G.f.: (x^3+9*x^2+x+3) / ((x-1)^2*(x+1)^2).
%F A261671 (End)
%t A261671 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 *)
%o A261671 (PARI) Vec((x^3+9*x^2+x+3)/((x-1)^2*(x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 13 2015
%Y A261671 Cf. A109732, A135730.
%K A261671 nonn,easy
%O A261671 0,1
%A A261671 _N. J. A. Sloane_, Sep 02 2015