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A092874 Decimal expansion of the "binary" Liouville number. 10


%S 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,

%T 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,

%U 7,2,3,3,8,0,3,9,4,5,9,5,6,3,3,4,1,3,6

%N Decimal expansion of the "binary" Liouville number.

%C 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.

%C 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.

%C According to the definitions introduced in A092855 and A051006, this number is "the binary mapping" of the sequence of factorials (A000142).

%H G. C. Greubel, <a href="/A092874/b092874.txt">Table of n, a(n) for n = 0..5000</a>

%H Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/aronsf.pdf">Binary mapping of monotonic sequences and the Aronson function</a>

%H Burkard Polster, <a href="https://www.youtube.com/watch?v=c9nUAXUSuII">Liouville's number, the easiest transcendental and its clones</a>, Mathologer video (2017).

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e .7656250596046447753906250000...

%t RealDigits[Sum[1/2^(n!), {n, Infinity}], 10, 105][[1]] (* _Alonso del Arte_, Dec 03 2012 *)

%o (PARI) { mt(v)= /*Returns the binary mapping of v monotonic sequence as a real in (0,1)*/

%o local(a=0.0,p=1,l);l=matsize(v)[2];

%o for(i=1,l,a+=2^(-v[i])); return(a)}

%o (PARI) suminf(n=2,2^-gamma(n)) \\ _Charles R Greathouse IV_, Jun 14 2020

%Y Cf. A092855, A051006.

%K easy,nonn,cons

%O 0,1

%A Ferenc Adorjan (fadorjan(AT)freemail.hu)

%E Offset corrected by _Franklin T. Adams-Watters_, Dec 14 2017

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)