A245254 Decimal expansion of U = Product_{k>=1} (k^(1/(k*(k+1)))), a Khintchine-like limiting constant related to Lüroth's representation of real numbers.

2, 2, 0, 0, 1, 6, 1, 0, 5, 8, 0, 9, 9, 0, 2, 6, 5, 5, 3, 1, 9, 4, 5, 5, 7, 8, 6, 6, 5, 5, 9, 9, 4, 4, 8, 7, 2, 6, 8, 5, 6, 6, 2, 3, 2, 4, 7, 5, 2, 7, 2, 3, 8, 8, 8, 7, 2, 3, 1, 4, 5, 1, 1, 7, 7, 6, 3, 1, 6, 9, 0, 1, 1, 2, 6, 9, 6, 6, 5, 9, 4, 7, 5, 8, 4, 7, 0, 2, 9, 7, 3, 4, 7, 2, 6, 8, 0, 7, 6, 2, 5, 8, 1, 6, 1

Offset

1,1

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=1..105.

Sofia Kalpazidou, Khintchine's constant for Lüroth representation, Journal of Number Theory, Vol. 29, No. 2 (June 1988), pp. 196-205.

Formula

U = exp(A085361).

U*V*W = 1, where V is A244109 and W is A131688.

Equals e * A085291. - Amiram Eldar, Jun 27 2021

Equals 1/A242624. - Amiram Eldar, Feb 06 2022

Example

2.200161058099026553194557866559944872685662324752723888723145117763169...

Maple

evalf(exp(Sum((Zeta(n+1)-1)/n, n=1..infinity)), 120); # Vaclav Kotesovec, Dec 11 2015

Mathematica

Exp[NSum[Log[k]/(k*(k+1)), {k, 1, Infinity}, WorkingPrecision -> 120, NSumTerms -> 5000, Method -> {NIntegrate, MaxRecursion -> 100}]] (* Vaclav Kotesovec, Dec 11 2015 *)

Crossrefs

Cf. A002210, A085291, A085361, A242624, A244109(V), A131688(W).

Sequence in context: A242249 A125226 A281790 * A059080 A062070 A347088

Adjacent sequences: A245251 A245252 A245253 * A245255 A245256 A245257

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 15 2014

Extensions

Corrected by Vaclav Kotesovec, Dec 11 2015

Status

approved