|
Search: id:A143607
|
|
|
| A143607 |
|
Numerators of principal and intermediate convergents to 2^(1/2). |
|
+0
3
|
|
| 1, 3, 4, 7, 10, 17, 24, 41, 58, 99, 140, 239, 338, 577, 816, 1393, 1970, 3363, 4756, 8119, 11482, 19601, 27720, 47321, 66922, 114243, 161564, 275807, 390050, 665857, 941664, 1607521, 2273378, 3880899, 5488420, 9369319, 13250218, 22619537
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The principal and intermediate convergents to 2^(1/2) begin with 1/1, 3/2 4/3, 7/5, 10/7; essentially, numerators=A143607, denominators=A002965.
|
|
REFERENCES
|
Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, New York, 1966.
Clark Kimberling, "Best lower and upper approximates to irrational numbers," Elemente der Mathematik, 52 (1997) 122-126.
|
|
CROSSREFS
|
Sequence in context: A134591 A058611 A098613 this_sequence A032715 A002887 A080034
Adjacent sequences: A143604 A143605 A143606 this_sequence A143608 A143609 A143610
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008
|
|
|
Search completed in 0.002 seconds
|
