OFFSET
1,1
COMMENTS
Recalling the Collatz map (cf. A006370 ) : x->x/2 if x is even; x->3x+1 if x is odd, let C_m(n) denotes the image of n after m iterations. Then b(n)= lim k -> infinity C_3k(n) (from the Collatz conjecture C_3k(n) is constant =1,2 or 4 for k large enough). Curiously the graph for a(n) presents "regularities" around zero and a pattern coming bigger and bigger. Compared with a random sequence of form : 7*n-3*sum(k=1,n,r(k)) where r(k) takes random values among (1;2;4).
EXAMPLE
since 3->10->5->16->8->4->2->1 etc. C_6(3)=2 and then for any k>=2 C_3k(3)=2, hence b(3)=2.
CROSSREFS
KEYWORD
sign
AUTHOR
Benoit Cloitre, Oct 30 2002
STATUS
approved