A080842 Numbers in the x/3 + 1 conjecture: Repeat until 1 is reached: if x is divisible by 3 then divide by 3, otherwise add 1.

1, 3, 1, 1, 5, 6, 2, 3, 1, 6, 2, 3, 1, 2, 3, 1, 8, 9, 3, 1, 9, 3, 1, 3, 1, 11, 12, 4, 5, 6, 2, 3, 1, 12, 4, 5, 6, 2, 3, 1, 4, 5, 6, 2, 3, 1, 14, 15, 5, 6, 2, 3, 1, 15, 5, 6, 2, 3, 1, 5, 6, 2, 3, 1, 17, 18, 6, 2, 3, 1, 18, 6, 2, 3, 1, 6, 2, 3, 1, 20, 21, 7, 8, 9, 3, 1, 21, 7, 8, 9, 3, 1, 7, 8, 9, 3, 1, 23, 24

Offset

1,2

Comments

These numbers converge to various last-3-digit endings and only two last-2-digit numbers: 2,1 or 3,1.

Links

Table of n, a(n) for n=1..99.

Example

The trajectories starting at x=2, 3, 4 etc. are (3,1), (1), (5,6,2,3,1), (6,2,3,1), (2,3,1), (8,9,3,1) etc. Each "1" marks the end of a trajectory.

Mathematica

Join[{1}, Flatten[Table[Rest[NestWhileList[If[Divisible[#, 3], #/3, #+1]&, n, #!=1&]], {n, 2, 30}]]] (* Harvey P. Dale, Feb 02 2012 *)

Prog

(PARI) mult3p1(n, p) = { print1(1" "); for(j=1, n, x=j; while(x>1, if(x%3==0, x/=3, x = x*p+1 ) ; print1(x" ") ; ); ) ; print1(" ") ; } { mult3p1(30, 1) ; } - R. J. Mathar, Feb 01 2008

Crossrefs

Cf. A080828, A067433.

Sequence in context: A294582 A294589 A204027 * A368211 A216948 A183944

Adjacent sequences: A080839 A080840 A080841 * A080843 A080844 A080845

Keyword

easy,nonn,tabf

Author

Cino Hilliard, Mar 28 2003

Extensions

Edited and corrected by R. J. Mathar, Feb 01 2008

Status

approved