|
| |
|
|
A118827
|
|
2-adic continued fraction of zero, where a(n) = if n=1(mod 2), +1, else -2*A006519(n/2).
|
|
5
|
|
|
|
1, -2, 1, -4, 1, -2, 1, -8, 1, -2, 1, -4, 1, -2, 1, -16, 1, -2, 1, -4, 1, -2, 1, -8, 1, -2, 1, -4, 1, -2, 1, -32, 1, -2, 1, -4, 1, -2, 1, -8, 1, -2, 1, -4, 1, -2, 1, -16, 1, -2, 1, -4, 1, -2, 1, -8, 1, -2, 1, -4, 1, -2, 1, -64, 1, -2, 1, -4, 1, -2, 1, -8, 1, -2, 1, -4, 1, -2, 1, -16, 1, -2, 1, -4, 1, -2, 1, -8, 1, -2, 1, -4, 1, -2, 1, -32, 1, -2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Limit of convergents equals zero; only the 6-th convergent is indeterminate. Other 2-adic continued fractions of zero are: A118821, A118824, A118830. A006519(n) is the highest power of 2 dividing n; A080277 = partial sums of A038712, where A038712(n) = 2*A006519(n) - 1.
|
|
|
LINKS
|
Table of n, a(n) for n=1..99.
|
|
|
EXAMPLE
|
For n>=1, convergents A118828(k)/A118829(k) are:
at k = 4*n: -1/(2*A080277(n));
at k = 4*n+1: -1/(2*A080277(n)-1);
at k = 4*n+2: -1/(2*A080277(n)-2);
at k = 4*n-1: 0.
Convergents begin:
1/1, -1/-2, 0/-1, -1/2, -1/1, 1/0, 0/1, 1/-8,
1/-7, -1/6, 0/-1, -1/10, -1/9, 1/-8, 0/1, 1/-24,
1/-23, -1/22, 0/-1, -1/26, -1/25, 1/-24, 0/1, 1/-32,
1/-31, -1/30, 0/-1, -1/34, -1/33, 1/-32, 0/1, 1/-64, ...
|
|
|
PROG
|
(PARI) a(n)=local(p=+1, q=-2); if(n%2==1, p, q*2^valuation(n/2, 2))
|
|
|
CROSSREFS
|
Cf. A006519, A080277; convergents: A118828/A118829; variants: A118821, A118824, A118830; A100338.
Sequence in context: A068057 A003484 * A118830 A055975 A006519 A087258
Adjacent sequences: A118824 A118825 A118826 * A118828 A118829 A118830
|
|
|
KEYWORD
|
cofr,sign
|
|
|
AUTHOR
|
Paul D. Hanna, May 01 2006
|
|
|
STATUS
|
approved
|
| |
|
|
