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 A118227 Decimal expansion of Cahen's constant. 3
 6, 4, 3, 4, 1, 0, 5, 4, 6, 2, 8, 8, 3, 3, 8, 0, 2, 6, 1, 8, 2, 2, 5, 4, 3, 0, 7, 7, 5, 7, 5, 6, 4, 7, 6, 3, 2, 8, 6, 5, 8, 7, 8, 6, 0, 2, 6, 8, 2, 3, 9, 5, 0, 5, 9, 8, 7, 0, 3, 0, 9, 2, 0, 3, 0, 7, 4, 9, 2, 7, 7, 6, 4, 6, 1, 8, 3, 2, 6, 1, 0, 8, 4, 8, 4, 4, 0, 8, 9, 5, 5, 5, 0, 4, 6, 3, 4, 3, 1, 9, 5, 4, 0, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Cahen proved that his constant is irrational. Davison and Shallit proved that it is transcendental and computed its simple continued fraction expansion A006280. - Jonathan Sondow, Aug 17 2014 LINKS E. Cahen, Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues, Nouvelles Annales de Mathematiques, 10 (1891), 508-514. J. L. Davison, Jeffrey Shallit, Continued Fractions for Some Alternating Series, Monatsh. Math., 111 (1991), 119-126. Eric Weisstein's World of Mathematics, Cahen's Constant FORMULA Sum_{k >= 0} (-1)^k/(A000058(k)-1). EXAMPLE 0.6434105462883380261... MATHEMATICA a[0] = 2; a[n_] := a[n] = a[n-1]^2 - a[n-1]+1; kmax = 1; FixedPoint[ RealDigits[ Sum[(-1)^k/(a[k]-1), {k, 0, kmax += 10}], 10, 105][[1]]&, kmax] (* Jean-François Alcover, Jul 28 2011, updated Jun 19 2014 *) CROSSREFS Cf. A000058, A006279, A006280, A006281, A123180, A242724. Sequence in context: A155044 A245634 A182618 * A199429 A235509 A224927 Adjacent sequences:  A118224 A118225 A118226 * A118228 A118229 A118230 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Apr 16 2006 STATUS approved

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Last modified October 13 19:48 EDT 2019. Contains 327981 sequences. (Running on oeis4.)