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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. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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, Volume 29, Issue 2, June 1988, Pages 196-205.

FORMULA

U = exp(A085361).

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

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, A085361, A244109(V), A131688(W).

Sequence in context: A242249 A125226 A281790 * A059080 A062070 A239395

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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)