|
| |
|
|
A143608
|
|
Numerators of the lower principal and intermediate convergents to 2^(1/2).
|
|
5
| |
|
|
1, 4, 7, 24, 41, 140, 239, 816, 1393, 4756, 8119, 27720, 47321, 161564, 275807, 941664, 1607521, 5488420, 9369319, 31988856, 54608393
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The lower principal and intermediate convergents to 2^(1/2), beginning with
1/1, 4/3, 7/5, 24/17, 41/29, form a strictly increasing sequence;
essentially, numerators=A143608 and denominators=A079496.
|
|
|
REFERENCES
| Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, New York, 1966.
|
|
|
LINKS
| John M. Campbell, An Integral Representation of Kekule' Numbers, and Double Integrals Related to Smarandache Sequences, Arxiv preprint arXiv:1105.3399, 2011.
Creighton Kenneth Dement, Comments on A143608 and A143609
C. Kimberling, Best lower and upper approximations to irrational numbers, Elem. Math. vol. 52 iss. 3 (1997) 122-126.
Index to sequences with linear recurrences with constant coefficients, signature (0,6,0,-1).
|
|
|
FORMULA
| Conjectures: a(n)=6*a(n-2)-a(n-4). G.f.: x*(1+4*x+x^2)/((x^2-2*x-1)*(x^2+2*x-1)). a(2n)=A005319(n). a(2n+1)=A002314(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]
|
|
|
CROSSREFS
| Sequence in context: A101824 A027946 A203230 * A079441 A129418 A073218
Adjacent sequences: A143605 A143606 A143607 * A143609 A143610 A143611
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008
|
| |
|
|
