A231097 Decimal expansion of the power tower of the ratio e/Pi.

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

Offset: 0

Author

Stanislav Sykora, Nov 06 2013

Keywords

• nonn
• cons
• easy

Comments

This infinite tetration limit of (e/Pi)^^n is also the only solution of x*(Pi/e)^x = 1.

Examples

			0.88036777898173462182674985...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Wikipedia, Lambert W function.
• Wikipedia, Tetration.

Crossrefs

Cf. A061360 (e/Pi), A231098 (tetration of Pi/e).

Programs

Mathematica

RealDigits[ProductLog[Log[Pi] - 1]/(Log[Pi] - 1), 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)

PARI

lambertw(log(Pi)-1)/(log(Pi)-1)

Formula

When 1/e^e <= c < 1, then c^c^c^... = LambertW(log(1/c))/log(1/c).