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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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).

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. Adams-Watters, Dec 14 2017

STATUS

approved

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Last modified April 22 12:53 EDT 2021. Contains 343177 sequences. (Running on oeis4.)