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A272286
Decimal expansion of Product_{k >= 1} (k*(k+1))^(-1/(k*(k+1))), a constant related to the alternating Lüroth representations of real numbers.
0
1, 2, 9, 2, 1, 5, 0, 1, 8, 4, 0, 6, 0, 9, 9, 8, 4, 1, 3, 4, 1, 5, 7, 1, 9, 0, 0, 0, 7, 4, 2, 1, 9, 7, 7, 7, 1, 5, 7, 3, 3, 6, 4, 6, 2, 0, 3, 8, 6, 7, 8, 7, 4, 4, 8, 7, 7, 3, 0, 0, 0, 6, 2, 5, 3, 9, 4, 0, 0, 9, 6, 1, 8, 2, 9, 7, 1, 0, 4, 2, 7, 5, 4, 0, 3, 9, 6, 8, 0, 5, 6, 7, 7, 5, 3, 6, 5, 4, 5, 1, 7, 7, 3, 3, 6
OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8.1 Alternative representations [of real numbers], p. 62.
LINKS
Sofia Kalpazidou, Khintchine's constant for Lüroth representation, Journal of Number Theory, Volume 29, Issue 2, June 1988, Pages 196-205.
FORMULA
Exp(-Sum_{n >= 1} (((1 + (-1)^(n+1))*Zeta(n+1) - 1)/n)). - After Vaclav Kotesovec's formula for A244109.
EXAMPLE
0.1292150184060998413415719000742197771573364620386787448773...
MATHEMATICA
digits = 105; Exp[-NSum[((1 + (-1)^(n + 1))*Zeta[n + 1] - 1)/n, {n, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> 2 digits, NSumTerms -> 200]] // RealDigits[#, 10, digits]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Offset corrected by Andrey Zabolotskiy, Dec 12 2023
STATUS
approved