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!)
A091809 Given the infinite continued fraction i+(i/(i+(i/(i+...)))), where i is the square root of (-1), this is the denominator of the imaginary part of the convergents. 7
1, 1, 2, 5, 3, 10, 41, 85, 178, 123, 769, 10, 3329, 533, 1602, 30005, 62441, 64970, 270409, 187575, 1171042, 2436961, 5071361, 16490, 1045821, 45703841, 95110562, 15225145, 411889609, 47619450, 1783745641, 3712008565, 7724760338 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The sequence of complex numbers (which this sequence is part of) converges to (i+sqrt(-1+4i))/2, found by simply solving the equation A=i+(i/A) for A using the quadratic formula. When plotted in the complex plane, these numbers form a counterclockwise spiral that quickly converges to a point.

LINKS

Table of n, a(n) for n=1..33.

EXAMPLE

a(6) = 10 since the sixth convergent is (3/5) + (13/10)i and hence the denominator of the imaginary part is 10.

MATHEMATICA

GenerateA091809[1] := I; GenerateA091809[n_] := I + I/(GenerateA091809[n-1]); GenerateDenominatorsA091809[n_] := Table[Denominator[Im[GenerateA091809[x]]], {x, 1, n}]; GenerateDenominatorsA091809[20] gives the first 20 terms.

A091809[n_] := Denominator[ IM[ Fold[ I/(I + #) &, 1, Range[n]]]]; Table[ A091809[n], {n, 0, 32}] (* Robert G. Wilson v, Mar 13 2004 *)

CROSSREFS

Cf. A091806, A091807, A091808.

Sequence in context: A097753 A120860 A259971 * A110315 A275677 A221183

Adjacent sequences:  A091806 A091807 A091808 * A091810 A091811 A091812

KEYWORD

cofr,frac,nonn

AUTHOR

Ryan Witko (witko(AT)nyu.edu), Mar 06 2004

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 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)