|
| |
|
|
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; 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*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
| Sequence in context: A077061 A072508 A075566 * A082486 A106591 A106592
Adjacent sequences: A076084 A076085 A076086 * A076088 A076089 A076090
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 30 2002
|
| |
|
|
