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A145571 Numerators of partial sums for Liouville's constant. 2
1, 11, 110001, 110001000000000000000001, 110001000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (list; graph; refs; listen; history; text; internal format)
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 Rosenberger-Fine 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

Table of n, a(n) for n=1..5.

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).

Sequence in context: A110780 A087395 A199169 * A049193 A216596 A079558

Adjacent sequences:  A145568 A145569 A145570 * A145572 A145573 A145574

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang Mar 06 2009

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)