

A076087


a(n)= 7*n  3*sum(i=1,n,b(i)) (see comment for b(i) definition).


0



4, 5, 6, 1, 4, 9, 8, 4, 3, 1, 4, 0, 4, 1, 6, 5, 1, 6, 11, 10, 9, 5, 1, 0, 5, 4, 0, 4, 8, 12, 13, 8, 3, 4, 5, 9, 13, 17, 18, 13, 14, 9, 4, 5, 6, 7, 2, 3, 1, 5, 9, 4, 1, 0, 1, 2, 3, 2, 7, 6, 5, 10, 15, 11, 7, 3, 1, 4, 9, 14, 10, 9, 8, 7, 12, 11, 10, 15, 20, 16, 15, 20, 25, 21, 17, 13, 9
(list;
graph;
refs;
listen;
history;
text;
internal format)



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*n3*sum(k=1,n,r(k)) where r(k) takes random values among (1;2;4).


LINKS

Table of n, a(n) for n=1..87.


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

Sequence in context: A077061 A072508 A075566 * A082486 A106591 A106592
Adjacent sequences: A076084 A076085 A076086 * A076088 A076089 A076090


KEYWORD

sign


AUTHOR

Benoit Cloitre, Oct 30 2002


STATUS

approved



