

A145571


Numerators of partial sums for Liouville's constant.


2




OFFSET

1,2


COMMENTS

The denominators are 10^(n!).
In a(n) the 1's appear at positions j!, j=1..n. Therefore Liouville's constant c:=Sum_{k>=1} 1/10^(k!) is the number 0.a(n) with n > infinity.
Liouville's constant c is transcendental. See, e.g., the proof in the RosenbergerFine reference.


REFERENCES

B. Fine and G. Rosenberger, Number theory: an introduction via the distribution of primes, Birkhäuser, Boston, Basel, Berlin, 2007. Th. 6.3.2.3., p. 286.


LINKS



FORMULA

a(n) = numerator(c(n)), with c(n):= Sum_{k=1..n} 1/10^(k!).


EXAMPLE

a(2)=11 because c(2)=1/10 + 1/100 = 11/100.
a(6) has 1's at positions 1,2,6,24,120,720 (A000142, factorials) and 0's in between.


CROSSREFS

Cf. A145572 (a(n) read as base 2 representation).


KEYWORD

nonn,frac,easy


AUTHOR



STATUS

approved



