

A092874


Decimal expansion of the "binary" Liouville number.


11



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

0,1


COMMENTS

The famous Liouville number is defined so that its nth 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 nth 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).


LINKS



EXAMPLE

.7656250596046447753906250000...= 1/2^1 +1/2^2 + 1/2^6 +1/2^24 + 1/2^120 +..


MATHEMATICA

RealDigits[Sum[1/2^(n!), {n, Infinity}], 10, 105][[1]] (* Alonso del Arte, Dec 03 2012 *)


PROG

(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)}


CROSSREFS



KEYWORD



AUTHOR

Ferenc Adorjan (fadorjan(AT)freemail.hu)


EXTENSIONS



STATUS

approved



