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A012245 Characteristic function of factorial numbers; also decimal expansion of Liouville's number or Liouville's constant). 6
1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Read as decimal fraction 1100010... in any base > 1 (arbitrary decimal point) Liouville's numbers are transcendental; read as a continued fraction it is also transcendental [G. H. Hardy and E. M. Wright, Th. 192].

a(A000142(n)) = 1; a(A063992(n)) = 0. [From Reinhard Zumkeller, Oct 11 2008]

REFERENCES

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 162.

T. W. Koerner, Fourier Analysis, Camb. Univ. Press 1988, p. 177.

J. Liouville, C. R. Acad. Sci. Paris 18, 883-885 and 993-995, 1844.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 58.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Index entries for characteristic functions

G. Xiao, Contfrac

Eric Weisstein's World of Mathematics, Liouville's Constant

Index entries for continued fractions for constants

FORMULA

G.f.: sum(i=1, oo, x^product(j=1, i, j)) - Jon Perry, Mar 31 2004

EXAMPLE

a(25) = a(26) =..= a(119) = 0 because 4! = 24 and 5! = 120

0.110001000000000000000001000000000000000000000000000000000000000000000... [From Harry J. Smith, May 15 2009]

MATHEMATICA

With[{nn=5}, ReplacePart[Table[0, {nn!}], Table[{n!}, {n, nn}]->1]] (* Harvey P. Dale, Jul 22 2012 *)

PROG

(PARI) { default(realprecision, 20080); x=10*suminf(n=1, 1.0/10^n!) + 1/10^20040; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b012245.txt", n, " ", d)); } [From Harry J. Smith, May 15 2009]

CROSSREFS

Cf. A000142, A058304 (continued fraction).

Sequence in context: A179020 A179771 A094875 * A185059 A179776 A089801

Adjacent sequences:  A012242 A012243 A012244 * A012246 A012247 A012248

KEYWORD

nonn,nice,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 23 15:56 EDT 2014. Contains 244869 sequences.