

A256500


Decimal expansion of the positive solution to x = 2*(1exp(x)).


5



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

1,2


COMMENTS

Each of the positive solutions to x = q*(1exp(x)) obtained for q = 2, 3, 4, and 5, appears in several formulas pertinent to Planck's blackbody radiation law. For a given q, the solution can be also written as q+W(q/exp(q)), where W is the Lambert function. Here q = 2.
The constant appears in asymptotic formula for A007820.  Vladimir Reshetnikov, Oct 10 2016


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
V. Kotesovec, Nonattacking chess pieces, 6ed, 2013, p. 249.
SpectralCalc, Calculation of Blackbody Radiance, Appendix C.
Wikipedia, Planck's law


EXAMPLE

1.5936242600400400923230418758751602417890024248188593649995...


MATHEMATICA

RealDigits[2 + LambertW[2 Exp[2]], 10, 100][[1]] (* Vladimir Reshetnikov, Oct 10 2016 *)


PROG

(PARI) a2=solve(x=0.1, 10, x2*(1exp(x))) \\ Use real precision in excess


CROSSREFS

Cf. A194567 (q=3), A256501 (q=4), A256502 (q=5).
Sequence in context: A216755 A255681 A021948 * A239545 A228402 A154265
Adjacent sequences: A256497 A256498 A256499 * A256501 A256502 A256503


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Mar 31 2015


STATUS

approved



