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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 (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
Burkard Polster, Liouville's number, the easiest transcendental and its clones, Mathologer video (2017).
Fedoua Sghiouer, Kacem Belhroukia, and Ali Kacha, Transcendence of some infinite series, arXiv preprint (2023). arXiv:2301.06495 [math.NT].
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)}
(PARI) suminf(n=2, 2^-gamma(n)) \\ Charles R Greathouse IV, Jun 14 2020
CROSSREFS
Sequence in context: A120634 A178753 A104178 * A198109 A059751 A019859
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 February 25 05:01 EST 2024. Contains 370310 sequences. (Running on oeis4.)