OFFSET
1,2
COMMENTS
Note that if k is in this sequence, then 2k is also. The plot shows a very narrow triangle of the possible halving/tripling pairs. As n increases, the width of the triangle grows on its right edge.
LINKS
EXAMPLE
For each integer k, let the ordered pair (h,t) give the numbers of halving and tripling steps in the Collatz trajectory of k. The pairs for k = 1..16 are (0,0), (1,0), (5,2), (2,0), (4,1), (6,2), (11,5), (3,0), (13,6), (5,1), (10,4), (7,2), (7,2), (12,5), (12,5), (4,0). Thus 13 and 15 are not in this sequence because their pairs are the same as for 12 and 14, respectively.
MATHEMATICA
Collatz[n_] := Module[{c1=0, c2=0, m=n}, While[m>1, If[EvenQ[m], c1++; m=m/2, c2++; m=3m+1]]; {c1, c2}]; s={}; t={}; n=0; While[Length[t]<100, n++; c=Collatz[n]; If[ !MemberQ[s, c], AppendTo[s, c]; AppendTo[t, n]]]; t
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 09 2007
STATUS
approved