A080842 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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