

A091807


Given the infinite continued fraction i+(i/(i+(i/(i+...)))), where i is the square root of (1), this is the denominator of the real part of the convergents.


7



1, 1, 2, 5, 3, 5, 41, 85, 178, 123, 769, 8, 3329, 533, 1602, 30005, 62441, 32485, 270409, 187575, 1171042, 2436961, 5071361, 26384, 1045821, 45703841, 95110562, 15225145, 411889609, 23809725, 1783745641, 3712008565, 7724760338
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OFFSET

0,3


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=0..32.


EXAMPLE

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


MATHEMATICA

GenerateA091807[1] := I; GenerateA091807[n_] := I + I/(GenerateA091807[n1]); GenerateDenominatorsA091807[n_] := Table[Denominator[Re[GenerateA091807[x]]], {x, 1, n}]; GenerateDenominatorsA091807[20] would give the first 20 terms.
A091807[n_] := Denominator[ Re[ Fold[ I/(I + #) &, 1, Range[n]]]]; Table[ A091807[n], {n, 0, 32}] (* Robert G. Wilson v, Mar 13 2004 *)


CROSSREFS

Cf. A091806, A091808, A091809.
Sequence in context: A299210 A104978 A124568 * A085825 A198140 A212614
Adjacent sequences: A091804 A091805 A091806 * A091808 A091809 A091810


KEYWORD

cofr,frac,nonn


AUTHOR

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


EXTENSIONS

More terms from Robert G. Wilson v, Mar 13 2004


STATUS

approved



