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

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

(PARI) apply(x->((x+lngamma(x))/log(x)), solve(x=2, 3, x*log(x)*(1+psi(x)) - (x+lngamma(x)))) \\ Michel Marcus, Mar 08 2023

Crossrefs

Sequence in context: A198234 A197385 A010596 * A131920 A180308 A155739

Adjacent sequences: A359696 A359697 A359698 * A359700 A359701 A359702

Keyword

cons,nonn

Author

Jodi Spitz, Mar 07 2023

Status

approved