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A328912
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Continued fraction expansion of log_2((sqrt(5)+1)/2) = 0.6942419... = A242208.
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8
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0, 1, 2, 3, 1, 2, 3, 2, 4, 2, 1, 2, 11, 2, 1, 11, 1, 1, 134, 2, 2, 2, 1, 4, 1, 1, 3, 1, 7, 1, 13, 1, 3, 5, 1, 1, 1, 8, 1, 3, 4, 1, 1, 1, 3, 4, 1, 3, 1, 4, 1, 4, 1, 3, 40, 1, 1, 5, 4, 3, 3, 1, 3, 1, 2, 6, 1, 1, 2, 28, 11, 1, 71, 2, 1, 4, 8, 5, 1, 2, 1, 1, 14
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OFFSET
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0,3
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COMMENTS
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This number is also the solution to 1 + 2^x = 4^x, or 1 + 1/2^x = 2^x, which clarifies the relation to Phi = (sqrt(5)+1)/2, solution to 1 + 1/x = x.
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LINKS
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EXAMPLE
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log_2((sqrt(5)+1)/2) = 0.6942419... = 0 + 1/(1 + 1/(2 + 1/(3 + 1/(1 + ...))))
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MATHEMATICA
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ContinuedFraction[Log2[GoldenRatio], 100] (* Paolo Xausa, Mar 07 2024 *)
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PROG
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(PARI) localprec(1000); contfrac(log(sqrt(5)+1)/log(2)-1)
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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