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A118227
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Decimal expansion of Cahen's constant.
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9
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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FORMULA
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Sum_{k >= 0} (-1)^k/(A000058(k)-1).
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EXAMPLE
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0.6434105462883380261...
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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