The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A224254 Full cycle lengths in the Collatz (3x+1) problem when the negative integers are used. 0
 2, 2, 2, 2, 5, 2, 5, 2, 5, 5, 2, 2, 5, 5, 2, 2, 18, 5, 5, 5, 2, 2, 18, 5, 5, 5, 2, 2, 2, 18, 18, 5, 5, 18, 5, 2, 5, 18, 2, 2, 18, 5, 2, 18, 18, 5, 5, 2, 5, 18, 5, 2, 2, 2, 2, 18, 5, 2, 2, 18, 18, 18, 2, 5, 2, 5, 18, 18, 5, 5, 2, 2, 2, 5, 5, 18, 2, 2, 2, 2, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are other cycles of lengths 2, 5 and 18 if negative integers are used. In Z, it is conjectured that the five values of cycle are 1, 2, 3, 5 and 18 (see A121510). LINKS Wikipedia, Collatz conjecture EXAMPLE a(1) = 2 because the cycle -1 -> -2 -> -1... contains 2 distinct terms; a(5) = 5 because the cycle -5 -> -14 -> -7->-20 -> -5 ... contains 5 distinct terms; a(17) = 18 because the cycle -17 -> -50 -> -25->-74 -> -37 -> -110 -> -55->-164 -> -82 -> -41 -> -122->-61 -> -182 -> -91 -> -272->-136 -> -68 -> -34 -> -17... contains 18 distinct terms. MAPLE nn:=1000:T:=array(1..nn): for n from -1 by -1 to -100 do:       x:=n:lst:={n}:k:=1:           for j from 1 to nn do:           T[j]:=0:           od:          T[1]:=n:             for it from 1 to 500 do:                if irem(x, 2)=0                then                x := x/2: lst:=lst union{x} :k:=k+1:T[k]:=x:               else               x := 3*x+1:  lst:=lst union{x}: k:=k+1:T[k]:=x :             fi:             od:             d:=nops(lst): z:=T[d]:z1:=3*z+1:ii:=0:               for i from 1 to d while(ii=0) do:                 if T[i]=z1                 then                 q:=d-i: printf(`%d, `, q+1):ii:=1:                else                fi:                od:                if ii=0 and T[d+1]=n                then                printf(`%d, `, d):                else           fi:      od: CROSSREFS Cf. A121510, A224166, A224183. Sequence in context: A130325 A154097 A221491 * A107604 A080647 A324516 Adjacent sequences:  A224251 A224252 A224253 * A224255 A224256 A224257 KEYWORD nonn AUTHOR Michel Lagneau, Apr 02 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)