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Search: id:A093725
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| A093725 |
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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. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sequence of complex numbers (which this sequence is part of) appears to converge to
1.529085513635746125160990523790225210619365... + i*0.74293413587832283909143193794726628109624299200...
Using Plouffe's Inverter, http://pi.lacim.uqam.ca/eng/, 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
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MATHEMATICA
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Table[ Re[ Numerator[ FromContinuedFraction[ Table[1 + I, {n}]]]], {n, 30}]
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CROSSREFS
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Cf. A091806, A091807, A091808, A091809, A093726, A093727.
Sequence in context: A164654 A072396 A001175 this_sequence A011413 A010629 A016671
Adjacent sequences: A093722 A093723 A093724 this_sequence A093726 A093727 A093728
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KEYWORD
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frac,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 11 2004
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