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.
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
Examples
0.1292150184060998413415719000742197771573364620386787448773...
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.
Programs
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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
Formula
Exp(-Sum_{n >= 1} (((1 + (-1)^(n+1))*Zeta(n+1) - 1)/n)). - After Vaclav Kotesovec's formula for A244109.
Extensions
Offset corrected by Andrey Zabolotskiy, Dec 12 2023