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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

Table of n, a(n) for n=0..104.

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 March 24 06:12 EDT 2017. Contains 283984 sequences.