The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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,frac,easy AUTHOR Wolfdieter Lang, Mar 06 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 14:49 EST 2023. Contains 367680 sequences. (Running on oeis4.)