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A371321
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Decimal expansion of Sum_{k>=0} 1/A007018(k).
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1
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1, 6, 9, 1, 0, 3, 0, 2, 0, 6, 7, 5, 7, 2, 5, 3, 9, 7, 4, 4, 3, 5, 6, 6, 2, 8, 4, 3, 1, 4, 5, 7, 4, 1, 7, 9, 3, 8, 0, 8, 5, 7, 7, 2, 4, 2, 5, 7, 9, 5, 2, 4, 9, 4, 4, 9, 6, 0, 4, 6, 6, 0, 5, 4, 0, 0, 0, 0, 5, 4, 3, 3, 8, 2, 4, 7, 3, 9, 6, 7, 9, 5, 6, 5, 8, 5, 4, 5, 6, 7, 8, 3, 1, 9, 0, 2, 1, 0, 3, 6, 5, 7, 0, 0, 3
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OFFSET
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1,2
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COMMENTS
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The corresponding alternating sum, Sum_{k>=0} (-1)^k/A007018(k), equals Cahen's constant (A118227).
Duverney et al. (2018) proved that this constant is transcendental.
Called the "Kellogg-Curtiss constant" by Sondow (2021), after the American mathematicians Oliver Dimon Kellogg (1878-1932) and David Raymond Curtiss (1878-1953).
The Engel expansion of this constant is 1 followed by the Sylvester sequence (A000058, see the Formula section).
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.7, p. 436.
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LINKS
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Jonathan Sondow, Irrationality and Transcendence of Alternating Series via Continued Fractions, in: A. Bostan and K. Raschel (eds.), Transcendence in Algebra, Combinatorics, Geometry and Number Theory, TRANS 2019. Springer Proceedings in Mathematics & Statistics, Vol. 373, Springer, Cham, 2021; arXiv preprint, arXiv:2009.14644 [math.NT], 2020.
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FORMULA
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Equals 1 + Sum_{k>=1} 1/(Product_{i=0..k-1} A000058(i)).
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EXAMPLE
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1.69103020675725397443566284314574179380857724257952...
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MATHEMATICA
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s[0] = 2; s[n_] := s[n] = s[n - 1]^2 - s[n - 1] + 1; kmax = 1; FixedPoint[RealDigits[Sum[1/(s[k] - 1), {k, 0, kmax += 10}], 10, 120][[1]] &, kmax] (* after Jean-François Alcover at A118227 *)
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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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