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A242208
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Decimal expansion of log_2(phi), the logarithm to base 2 of phi, the "golden ratio" (1+sqrt(5))/2.
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17
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6, 9, 4, 2, 4, 1, 9, 1, 3, 6, 3, 0, 6, 1, 7, 3, 0, 1, 7, 3, 8, 7, 9, 0, 2, 6, 6, 8, 9, 8, 5, 9, 5, 2, 2, 3, 4, 6, 3, 5, 6, 7, 2, 8, 5, 2, 2, 7, 1, 2, 9, 7, 1, 5, 9, 8, 0, 9, 8, 9, 8, 6, 6, 5, 4, 1, 4, 0, 5, 7, 4, 4, 1, 0, 5, 0, 1, 1, 7, 6, 1, 8, 9, 7, 6, 3, 1, 4, 1, 7, 2, 3, 4, 7, 6, 4, 5, 3, 5, 9
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OFFSET
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0,1
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COMMENTS
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The limiting fractal dimension of a pattern generated by cellular automaton rule 150 is 1+log_2(phi).
This number is also involved in the evaluation of asymptotics for the number of odd terms in Pascal's trinomial triangle.
Also, the solution to 1 + 2^x = 4^x. See A328900 for solution to 2^x + 3^x = 4^x. - M. F. Hasler, Oct 30 2019
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LINKS
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FORMULA
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log((1 + sqrt(5))/2)/log(2).
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EXAMPLE
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0.6942419136306173017387902668985952234635672852271297159809898665414...
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MATHEMATICA
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RealDigits[Log[2, GoldenRatio], 10, 100] // First
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PROG
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(PARI) print(c=log(sqrt(5)+1)/log(2)-1); digits(c\.1^default(realprecision))[^-1] \\ [^-1] to discard possibly incorrect last digit. Use e.g. \p999 to get more digits. - M. F. Hasler, Oct 30 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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