login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041550 Numerators of continued fraction convergents to sqrt(293). 10
17, 137, 154, 291, 2482, 84679, 679914, 764593, 1444507, 12320649, 420346573, 3375093233, 3795439806, 7170533039, 61159704118, 2086600473051, 16753963488526, 18840563961577, 35594527450103, 303596783562401, 10357885168571737, 83166678132136297 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Johannes W. Meijer, Jun 12 2010: (Start)

The a(n) terms of this sequence can be constructed with the terms of sequence A090306.

For the terms of the periodical sequence of the continued fraction for sqrt(293) see A040275. We observe that its period is five. (End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 4964, 0, 0, 0, 0, 1).

FORMULA

From Johannes W. Meijer, Jun 12 2010: (Start)

a(5n) = A090306(3n+1), a(5n+1) = (A090306(3n+2) - A090306(3n+1))/2, a(5n+2) = (A090306(3n+2) + A090306(3n+1))/2, a(5n+3) = A090306(3n+2) and a(5n+4) = A090306(3n+3)/2. (End)

G.f.: -(x^9-17*x^8+137*x^7-154*x^6+291*x^5+2482*x^4+291*x^3+154*x^2+137*x+17) / (x^10+4964*x^5-1). - Colin Barker, Nov 08 2013

MATHEMATICA

Numerator[Convergents[Sqrt[293], 30]] (* Vincenzo Librandi, Nov 04 2013 *)

CROSSREFS

Cf. A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550, A041551.

Sequence in context: A022612 A205815 A060220 * A142788 A244874 A085958

Adjacent sequences:  A041547 A041548 A041549 * A041551 A041552 A041553

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 08 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 03:06 EST 2019. Contains 320364 sequences. (Running on oeis4.)