

A092874


Decimal expansion of the "binary" Liouville number.


10



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

G. C. Greubel, Table of n, a(n) for n = 0..5000
Ferenc Adorjan, Binary mapping of monotonic sequences and the Aronson function
Burkard Polster, Liouville's number, the easiest transcendental and its clones, Mathologer video (2017).
Index entries for transcendental numbers


EXAMPLE

.7656250596046447753906250000...


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)}
(PARI) suminf(n=2, 2^gamma(n)) \\ Charles R Greathouse IV, Jun 14 2020


CROSSREFS

Cf. A092855, A051006.
Sequence in context: A120634 A178753 A104178 * A198109 A059751 A019859
Adjacent sequences: A092871 A092872 A092873 * A092875 A092876 A092877


KEYWORD

easy,nonn,cons


AUTHOR

Ferenc Adorjan (fadorjan(AT)freemail.hu)


EXTENSIONS

Offset corrected by Franklin T. AdamsWatters, Dec 14 2017


STATUS

approved



