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A329810
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Decimal expansion of the constant whose continued fraction representation is [0; 1, 3, 7, 15, 31, ...] = A000225 (the Mersenne numbers).
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0
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7, 5, 8, 5, 4, 2, 3, 0, 8, 1, 7, 1, 0, 5, 5, 7, 3, 9, 2, 6, 8, 1, 2, 6, 0, 4, 8, 8, 4, 2, 2, 4, 8, 8, 9, 3, 4, 2, 1, 2, 4, 7, 7, 7, 9, 7, 9, 6, 9, 5, 2, 8, 6, 0, 2, 9, 9, 5, 5, 2, 3, 9, 4, 0, 3, 1, 9, 0, 9, 5, 3, 5, 0, 9, 0, 9, 4, 0, 6, 7, 2, 3, 0, 8, 5, 9, 8
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OFFSET
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0,1
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COMMENTS
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Since Mersenne numbers of the form 2^x - 1 consist entirely of 1's when written in binary, this continued fraction is nothing but 1's if written in binary.
Binary continued fraction: 1/(1+1/(11+1/(111+1/(1111+1/(11111+1/(111111+1/...
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LINKS
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EXAMPLE
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0.758542308171055739268126048842248893421247779...
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MATHEMATICA
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N[FromContinuedFraction[Table[2^k - 1, {k, 0, 100}]], 120] (* Vaclav Kotesovec, Nov 21 2019 *)
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PROG
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(PARI) dec_exp(v)= w=contfracpnqn(v); w[1, 1]/w[2, 1]+0.
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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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