A093725 Given the infinite continued fraction (1+i)+((1+i)/(1+i)+((1+i)/((1+i)+...)))), where i is the square root of (-1), this is the numerator of the real part of the convergents.

1, 3, 8, 6, 23, 199, 576, 208, 4809, 4633, 40168, 29022, 335501, 33435, 62272, 506164, 23405457, 67643027, 195491976, 47081858, 39825101, 4718963799, 13638058496, 4926840072, 5424316981, 329207907547, 951428510952, 23704133014

Offset

1,2

Comments

The sequence of complex numbers (which this sequence is part of) appears to converge to

1.529085513635746125160990523790225210619365... + i*0.74293413587832283909143193794726628109624299200...

Using Plouffe's Inverter yields:

Roots of polynomials of 5th degree (coeffs: -9..9) 1529085513635746 = 1+1*x-4*x^2-6*x^3+4*x^4+4*x^5

Roots of polynomials of 5th degree (coeffs: -9..9) 7429341358783228 = 1+5*x+4*x^2-2*x^3-4*x^4-4*x^5

Links

Table of n, a(n) for n=1..28.

Simon Plouffe, Plouffe's Inverter

Mathematica

Table[ Re[ Numerator[ FromContinuedFraction[ Table[1 + I, {n}]]]], {n, 30}]

Crossrefs

Cf. A091806, A091807, A091808, A091809, A093726, A093727.

Sequence in context: A366612 A072396 A001175 * A347118 A306933 A316565

Adjacent sequences: A093722 A093723 A093724 * A093726 A093727 A093728

Keyword

frac,nonn

Author

Robert G. Wilson v, Mar 11 2004

Status

approved