A168222 a(n) = A006369(A006369(n)).

0, 1, 2, 3, 7, 9, 5, 6, 15, 4, 17, 10, 11, 23, 25, 13, 14, 31, 8, 33, 18, 19, 39, 41, 21, 22, 47, 12, 49, 26, 27, 55, 57, 29, 30, 63, 16, 65, 34, 35, 71, 73, 37, 38, 79, 20, 81, 42, 43, 87, 89, 45, 46, 95, 24, 97, 50, 51, 103, 105, 53, 54, 111, 28, 113, 58, 59, 119, 121, 61, 62

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2009

Keywords

• nonn

Comments

Inverse integer permutation to A168221;

a(A006368(n)) = A006369(n).

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences related to 3x+1 (or Collatz) problem

Programs

Mathematica

Table[Nest[If[Divisible[#,3],2#/3,Round[4#/3]]&,n,2],{n,0,100}] (* Paolo Xausa, Dec 15 2023 *)

Formula

Conjectures from Colin Barker, Aug 15 2019: (Start)

G.f.: x*(1 + 2*x + 3*x^2 + 7*x^3 + 9*x^4 + 5*x^5 + 6*x^6 + 15*x^7 + 4*x^8 + 15*x^9 + 6*x^10 + 5*x^11 + 9*x^12 + 7*x^13 + 3*x^14 + 2*x^15 + x^16) / ((1 - x)^2*(1 + x + x^2)^2*(1 + x^3 + x^6)^2).

a(n) = 2*a(n-9) - a(n-18) for n>17.

(End)