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A092874
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Decimal expansion of the "binary" Liouville number.
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12
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7, 6, 5, 6, 2, 5, 0, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 5, 2, 3, 1, 6, 3, 8, 4, 5, 2, 6, 2, 6, 4, 0, 0, 5, 0, 9, 9, 9, 9, 1, 3, 8, 3, 8, 2, 2, 2, 3, 7, 2, 3, 3, 8, 0, 3, 9, 4, 5, 9, 5, 6, 3, 3, 4, 1, 3, 6
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OFFSET
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0,1
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COMMENTS
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The famous Liouville number is defined so that its n-th fractional decimal digit is 1 if and only if there exists k, such that k! = n.
The binary Liouville number is defined similarly, but as a binary number: its n-th fractional binary digit is 1 if and only if there exists k, such that k! = n.
According to the definitions introduced in A092855 and A051006, this number is "the binary mapping" of the sequence of factorials (A000142).
For the numerators of the partial sums of B(n) := Sum_{j=1..n} 1/j^(n!) see A145572. - Wolfdieter Lang, Apr 10 2024
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LINKS
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EXAMPLE
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.7656250596046447753906250000...= 1/2^1 +1/2^2 + 1/2^6 +1/2^24 + 1/2^120 +..
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MATHEMATICA
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RealDigits[Sum[1/2^(n!), {n, Infinity}], 10, 105][[1]] (* Alonso del Arte, Dec 03 2012 *)
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PROG
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(PARI) { mt(v)= /*Returns the binary mapping of v monotonic sequence as a real in (0, 1)*/
local(a=0.0, p=1, l); l=matsize(v)[2];
for(i=1, l, a+=2^(-v[i])); return(a)}
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CROSSREFS
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KEYWORD
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AUTHOR
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Ferenc Adorjan (fadorjan(AT)freemail.hu)
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EXTENSIONS
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STATUS
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approved
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