%I #7 Dec 10 2015 02:38:38
%S 1,1,2,5,3,5,41,85,178,123,769,8,3329,533,1602,30005,62441,32485,
%T 270409,187575,1171042,2436961,5071361,26384,1045821,45703841,
%U 95110562,15225145,411889609,23809725,1783745641,3712008565,7724760338
%N 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.
%C 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.
%e a(6) = 5 since the sixth convergent is (3/5) + (13/10)i and hence the denominator of the real part is 5.
%t GenerateA091807[1] := I; GenerateA091807[n_] := I + I/(GenerateA091807[n-1]); GenerateDenominatorsA091807[n_] := Table[Denominator[Re[GenerateA091807[x]]], {x, 1, n}]; GenerateDenominatorsA091807[20] would give the first 20 terms.
%t A091807[n_] := Denominator[ Re[ Fold[ I/(I + #) &, 1, Range[n]]]]; Table[ A091807[n], {n, 0, 32}] (* _Robert G. Wilson v_, Mar 13 2004 *)
%Y Cf. A091806, A091808, A091809.
%K cofr,frac,nonn
%O 0,3
%A Ryan Witko (witko(AT)nyu.edu), Mar 06 2004
%E More terms from _Robert G. Wilson v_, Mar 13 2004