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A202501 Decimal expansion of x satisfying x=e^(-Pi*x/2). 5
4, 7, 4, 5, 4, 0, 9, 9, 9, 5, 1, 2, 6, 5, 1, 1, 2, 3, 0, 1, 7, 4, 6, 7, 9, 4, 4, 0, 4, 8, 2, 1, 2, 4, 5, 1, 1, 4, 9, 1, 0, 7, 6, 8, 0, 6, 5, 9, 9, 2, 6, 7, 1, 4, 0, 9, 8, 1, 3, 7, 9, 7, 2, 2, 7, 0, 6, 8, 8, 5, 5, 9, 8, 9, 9, 3, 3, 0, 8, 8, 5, 9, 8, 3, 1, 1, 4, 9, 3, 2, 0, 7, 0, 0, 5, 9, 0, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A202348 for a guide to related sequences.  The Mathematica program includes a graph.

Also the only solution of x=I^(x*I), since I^I = exp(-Pi/2). Also the infinite power tower (tetration) of I^I, i.e., the convergent sequence I^(I*I^(I*I^(...(I*I^I)...))). Also LambertW(Pi/2)/(Pi/2). - Stanislav Sykora, Nov 06 2013

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Steven R. Finch, Tauberian Constants, August 30, 2004 [Cached copy, with permission of the author]

EXAMPLE

x=0.474540999512651123017467944048212451149107680...

MATHEMATICA

u = -Pi/2; v = 0;

f[x_] := x; g[x_] := E^(u*x + v)

Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]

RealDigits[r]    (* A202501 *)

RealDigits[ 2*ProductLog[Pi/2]/Pi, 10, 99] // First (* Jean-Fran├žois Alcover, Feb 27 2013 *)

PROG

(PARI) lambertw(Pi/2)/(Pi/2) \\ Stanislav Sykora, Nov 06 2013

CROSSREFS

Cf. A202348, A049006, A231095 (comment).

Sequence in context: A005472 A111522 A019735 * A195362 A106739 A112677

Adjacent sequences:  A202498 A202499 A202500 * A202502 A202503 A202504

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 20 2011

STATUS

approved

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Last modified April 5 23:12 EDT 2020. Contains 333260 sequences. (Running on oeis4.)