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A065918
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Decimal expansion of log(2 + sqrt(3)).
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5
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1, 3, 1, 6, 9, 5, 7, 8, 9, 6, 9, 2, 4, 8, 1, 6, 7, 0, 8, 6, 2, 5, 0, 4, 6, 3, 4, 7, 3, 0, 7, 9, 6, 8, 4, 4, 4, 0, 2, 6, 9, 8, 1, 9, 7, 1, 4, 6, 7, 5, 1, 6, 4, 7, 9, 7, 6, 8, 4, 7, 2, 2, 5, 6, 9, 2, 0, 4, 6, 0, 1, 8, 5, 4, 1, 6, 4, 4, 3, 9, 7, 6, 0, 7, 4, 2, 1, 9, 0, 1, 3, 4, 5, 0, 1, 0, 1, 7, 8, 3, 5, 5
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OFFSET
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1,2
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COMMENTS
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x = 2^n - 1 is prime if and only if x divides cosh(2^(n - 2)*log(2 + sqrt(3))).
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LINKS
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FORMULA
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Equals arccosh(2) since arccosh(x) = log(x + sqrt(x^2 - 1)). - Stanislav Sykora, Nov 01 2013
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EXAMPLE
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1.316957896924816708625046347307968444...
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 2080); x=log(2 + sqrt(3)); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065918.txt", n, " ", d)) \\ Harry J. Smith, Nov 04 2009
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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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