A300904 Decimal expansion of the positive solution to Pi^x = Pi + x.

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

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Lambert W-Function.

Eric Weisstein's World of Mathematics, Pi.

Wikipedia, Lambert W function.

Wikipedia, Pi.

Formula

Equals -(log(Pi)*Pi+LambertW(-1, -log(Pi)*exp(-log(Pi)*Pi)))/log(Pi).

Example

1.30311436056414282237568004579571932219648879925328977038807684...

Maple

Digits:= 200:
evalf(-(log(Pi)*Pi+LambertW(-1, -log(Pi)*exp(-log(Pi)*Pi)))/log(Pi));

Mathematica

RealDigits[Pi + LambertW[-1, -Log[Pi]*Exp[-Log[Pi]*Pi]]/Log[Pi], 10, 120][[1]] (* Amiram Eldar, Apr 13 2026 *)

Prog

(PARI) localprec(9+N=100); digits(solve(x=1, 1.5, Pi+x-Pi^x)*10^N\1) \\ M. F. Hasler, Apr 13 2026

Crossrefs

Cf. A000796, A280722.

Sequence in context: A051171 A336118 A342639 * A307807 A350849 A318504

Adjacent sequences: A300901 A300902 A300903 * A300905 A300906 A300907

Keyword

nonn,cons

Author

Alois P. Heinz, Mar 14 2018

Status

approved