login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195680 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(12). 4
7, 2772, 5945, 26144, 285621, 257076560, 2386970016, 103850955649, 254621037540, 3060691213613, 29733959304728, 62837775720000, 89511043811115, 453985767379732, 1567652657852541, 35830073055128140, 22926879590846577132 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..17.

MATHEMATICA

r = Sqrt[12]; z = 24;

p[{f_, n_}] := (#1[[2]]/#1[[

      1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[

         2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[

     Array[FromContinuedFraction[

        ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];

{a, b} = ({Denominator[#1], Numerator[#1]} &)[

  p[{r, z}]]  (* A195680, A195681 *)

Sqrt[a^2 + b^2] (* A195682 *)

(* Peter J. C. Moses, Sep 02 2011 *)

CROSSREFS

Cf. A195500, A195681, A195682.

Sequence in context: A203705 A178172 A234621 * A203587 A077721 A235464

Adjacent sequences:  A195677 A195678 A195679 * A195681 A195682 A195683

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 22 2011

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 June 21 19:59 EDT 2021. Contains 345365 sequences. (Running on oeis4.)