A141606 -id:A141606 - cp's OEIS frontend

A143913 Continued fraction expansion of e^(W(e-1)/(e-1)) where W(z) denotes the Lambert W function and e = 2.718281828...

1, 1, 1, 2, 1, 2, 5, 5, 1, 554, 3, 4, 1, 23, 2, 9, 2, 1, 305, 1, 1, 1, 3, 5, 5, 1, 3, 10, 5, 3, 1, 2, 1, 2, 1, 1, 2, 1, 4, 2, 1, 3, 2, 9, 1, 4, 11, 1, 3, 1, 3, 3, 1, 11, 4, 4, 1, 1, 2, 2, 3, 3, 4, 1, 3, 6, 3, 1, 2, 1, 3, 3, 3, 9, 1, 2, 11, 7, 1, 4, 1, 8, 10, 23, 2, 4, 1, 2, 10, 5, 2, 5, 1, 3, 36, 1, 6, 1, 6

Offset: 0

Ross La Haye, Sep 04 2008

G. C. Greubel, Table of n, a(n) for n = 0..9999

Cf. A141606 for decimal expansion.

Cf. A143914, A143915.

ContinuedFraction[E^((ProductLog[E - 1])/(E - 1)), 111]

contfrac(exp((lambertw(exp(1) -1)/(exp(1) -1)))) \\ G. C. Greubel, Mar 02 2018

Offset changed by Andrew Howroyd, Aug 09 2024

A143914 Numerators of continued fraction convergents to e^(W(e-1)/(e-1)) where W(z) denotes the Lambert W function and e = 2.718281828...

Original entry on oeis.org

1, 2, 3, 8, 11, 30, 161, 835, 996, 552619, 1658853, 7188031, 8846884, 210666363, 430179610, 4082282853, 8594745316, 12677028169, 3875088336861, 3887765365030, 7762853701891, 11650619066921, 42714710902654

Offset: 0

Ross La Haye, Sep 05 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A141606 for decimal expansion, A143913 for continued fraction expansion.

Cf. A143915

Table[Numerator[FromContinuedFraction[ContinuedFraction[E^((ProductLog[E - 1])/(E - 1)), n]]], {n, 1, 25}]

A143915 Denominators of continued fraction convergents to e^(W(e-1)/(e-1)) where W(z) denotes the Lambert W function and e = 2.718281828...

Original entry on oeis.org

1, 1, 2, 5, 7, 19, 102, 529, 631, 350103, 1050940, 4553863, 5604803, 133464332, 272533467, 2586265535, 5445064537, 8031330072, 2455000736497, 2463032066569, 4918032803066, 7381064869635, 27061227411971, 142687201929490

Offset: 0

Ross La Haye, Sep 05 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A143914 (numerators), A141606 (decimal expansion), A143913 (continued fraction).

Table[Denominator[FromContinuedFraction[ContinuedFraction[E^((ProductLog[E - 1])/(E - 1)), n]]], {n, 1, 25}]

A375596 Decimal expansion of 1/(1 - W(1/e)), where W is the Lambert W function.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Aug 20 2024

			1.38593327599819425386062181488251586064513...

Edgar Assing, On gaps between primes. See p. 45.

Cf. A202357.

Cf. A141606, A299617, A299618, A299619, A299632, A299633, A307951, A322166.

RealDigits[1/(1-ProductLog[1/E]),10,100][[1]]

1/(1-lambertw(1/exp(1))) \\ Michel Marcus, Aug 20 2024

Equals 1/(1 - A202357).

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A143913 Continued fraction expansion of e^(W(e-1)/(e-1)) where W(z) denotes the Lambert W function and e = 2.718281828...

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A143914 Numerators of continued fraction convergents to e^(W(e-1)/(e-1)) where W(z) denotes the Lambert W function and e = 2.718281828...

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A143915 Denominators of continued fraction convergents to e^(W(e-1)/(e-1)) where W(z) denotes the Lambert W function and e = 2.718281828...

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A375596 Decimal expansion of 1/(1 - W(1/e)), where W is the Lambert W function.

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