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 A118227 Decimal expansion of Cahen's constant. 9
 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 Named after the French mathematician Eugène Cahen (1865 - 1941). - Amiram Eldar, Oct 29 2020 LINKS Table of n, a(n) for n=0..104. Eugène Cahen, Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues, Nouvelles Annales de Mathématiques, Vol. 10 (1891), pp. 508-514. J. L. Davison and Jeffrey Shallit, Continued Fractions for Some Alternating Series, Monatsh. Math., Vol. 111, No. 2 (1991), pp. 119-126, alternative link. Eric Weisstein's World of Mathematics, Cahen's Constant. Wikipedia, Cahen's constant. Index entries for transcendental numbers FORMULA Sum_{k >= 0} (-1)^k/(A000058(k)-1). Equals Sum_{n>=0} 1/A000058(2*n) = 1 - Sum_{n>=0} 1/A000058(2*n+1). - Amiram Eldar, Oct 29 2020 Equals 1 + (1/2) * Sum_{n>=0} (-1)^(n+1)/A129871(n). - Bernard Schott, Apr 06 2021 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 *) PROG (PARI) C=1; 1+suminf(k=1, C+=C^2; (-1)^k/C) \\ Charles R Greathouse IV, Jul 14 2020 CROSSREFS Cf. A000058, A006279, A006280, A006281, A123180, A129871, A242724. Sequence in context: A155044 A245634 A182618 * A199429 A235509 A346696 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 April 16 21:50 EDT 2024. Contains 371755 sequences. (Running on oeis4.)