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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 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

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Last modified February 28 11:08 EST 2020. Contains 332323 sequences. (Running on oeis4.)