

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.


0



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
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OFFSET

1,2


COMMENTS

These numbers converge to various last3digit endings and only two last2digit numbers: 2,1 or 3,1.


LINKS



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



KEYWORD

easy,nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



