OFFSET
1,4
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
Robert G. Wilson v, Table of n, a(n) for n = 1..1002
EXAMPLE
a(6) = 3 since the sixth convergent is (3/5) + (13/10)i and hence the numerator of the real part is 3.
MAPLE
A091806 := proc(n)
numtheory[cfrac]([I, [I, I]$n-1]) ;
numer(Re(%)) ;
end proc:
seq(A091806(n), n=1..100) ; # Robert Israel, Mar 14 2016
MATHEMATICA
GenerateA091806[1] := I; GenerateA091806[n_] := I + I/(GenerateA091806[n-1]); GenerateNumeratorsA091806[n_] := Table[Numerator[Re[GenerateA091806[x]]], {x, 1, n}]; (* GenerateNumeratorsA091806[20] would give the first 20 terms. *)
A091806[n_] := Numerator[ Re[ Fold[ I/(I + #) &, 1, Range[n]]]]; Table[ A091806[n], {n, 0, 32}] (* Robert G. Wilson v, Mar 13 2004 *)
CROSSREFS
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