The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A376660 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A376660

Decimal expansion of a constant related to the asymptotics of A376630 and A376631.
(history; published version)

#13 by Vaclav Kotesovec at Tue Oct 08 09:36:15 EDT 2024

STATUS

editing

approved

#12 by Vaclav Kotesovec at Tue Oct 08 09:36:11 EDT 2024

FORMULA

Equals exp(sqrt(3*log(r)^2/4 + 2*polylog(2, r^(1/2)) - Pi^2/6), ), where r = A088559 = 0.4655712318767680266567312252199... is the real root of the equation r*(1+r)^2 = 1. - Vaclav Kotesovec, Oct 07 2024

STATUS

approved

editing

#11 by Vaclav Kotesovec at Mon Oct 07 15:35:54 EDT 2024

STATUS

editing

approved

#10 by Vaclav Kotesovec at Mon Oct 07 15:35:19 EDT 2024

DATA

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

#9 by Vaclav Kotesovec at Mon Oct 07 15:33:31 EDT 2024

FORMULA

Equals exp(sqrt(3*log(r)^2/4 + 2*polylog(2, r^(1/2)) - Pi^2/6), where r = A088559 = 0.4655712318767680266567312252199... is the real root of the equation r*(1+r)^2 = 1. - Vaclav Kotesovec, Oct 07 2024

CROSSREFS

Cf. A088559.

#8 by Vaclav Kotesovec at Mon Oct 07 15:32:39 EDT 2024

MATHEMATICA

RealDigits[E^Sqrt[3*Log[r]^2/4 + 2*PolyLog[2, r^(1/2)] - Pi^2/6] /. r -> (-2 + ((29 - 3*Sqrt[93])/2)^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))/3, 10, 120][[1]] (* Vaclav Kotesovec, Oct 07 2024 *)

STATUS

approved

editing

#7 by Vaclav Kotesovec at Sun Oct 06 10:45:18 EDT 2024

STATUS

editing

approved

#6 by Vaclav Kotesovec at Sun Oct 06 10:45:15 EDT 2024

CROSSREFS

Cf. A333198, A376621, A376630, A376631, A376658, A376659, A376815.

STATUS

approved

editing

#5 by Vaclav Kotesovec at Sun Oct 06 10:33:06 EDT 2024

STATUS

editing

approved

#4 by Vaclav Kotesovec at Sun Oct 06 10:31:31 EDT 2024

FORMULA

Equals A376815^(1/2). - Vaclav Kotesovec, Oct 06 2024

STATUS

approved

editing