A359699 - OEIS

A359699

Decimal expansion of x such that Gamma(t) and t^x*e^-t are tangent at one point.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..106.

Math Stack Exchange, For what z do Gamma(x) and x^z e^-x share a tangent line at exactly one point?

EXAMPLE

2.885182122499993175519796224373851235141...

MATHEMATICA

x[t_] := t*(1 + PolyGamma[0, t]);

x[t] /. FindRoot[Gamma[t] == Exp[-t]*t^x[t], {t, 2}, WorkingPrecision -> 106] // RealDigits // First (* Jean-François Alcover, Mar 08 2023 *)

PROG