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A202345
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Decimal expansion of x < 0 satisfying 2*x + 2 = exp(x).
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3
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7, 6, 8, 0, 3, 9, 0, 4, 7, 0, 1, 3, 4, 6, 5, 5, 6, 5, 2, 5, 5, 6, 8, 3, 5, 2, 6, 0, 7, 7, 5, 4, 7, 9, 9, 0, 9, 0, 6, 8, 4, 9, 1, 4, 8, 8, 7, 1, 9, 1, 8, 1, 9, 4, 5, 1, 0, 3, 1, 0, 3, 2, 7, 2, 4, 8, 3, 7, 8, 8, 9, 0, 1, 2, 7, 6, 2, 3, 4, 2, 0, 7, 0, 9, 1, 4, 5, 1, 3, 9, 0, 2, 0, 3, 3, 9, 5, 2, 6
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OFFSET
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0,1
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COMMENTS
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See A202320 for a guide to related sequences. The Mathematica program includes a graph.
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LINKS
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FORMULA
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EXAMPLE
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x<0: -0.76803904701346556525568352607754...
x>0: 1.678346990016660653412884512094523...
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MATHEMATICA
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u = 2; v = 2;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[-1 - LambertW[-Exp[-1]/2], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)
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PROG
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(PARI) solve(x=-1, 0, 2*x+2-exp(x)) \\ Michel Marcus, Nov 09 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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