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

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8.1 Alternative representations [of real numbers], p. 62.

Links

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

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

Cf. A131688, A244109, A245254.

Sequence in context: A249270 A153739 A298589 * A019645 A011065 A088540

Adjacent sequences: A272283 A272284 A272285 * A272287 A272288 A272289

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 24 2016

Extensions

Offset corrected by Andrey Zabolotskiy, Dec 12 2023

Status

approved