A030437 Decimal expansion of x such that x^x = Pi.

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

Offset: 1

Author

James L. Dean (csvcjld(AT)nomvs.lsumc.edu)

Keywords

• nonn
• cons

Examples

			x = 1.8541059679210264327483707184102932454292... .
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000796 (Pi), A100947 (continued fraction), A073243 (reciprocal).

Programs

Maple

x^x=Pi; solve(%,x); evalf(%, 140); # solution is log(Pi)/LambertW(log(Pi)), where LambertW is the Omega function.

Mathematica

x=Pi; RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2010 *)
RealDigits[x/.FindRoot[x^x==Pi,{x,1},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Nov 29 2024 *)

PARI

solve(x=1, 2, x^x-Pi) \\ Michel Marcus, Jan 14 2015

PARI

exp(lambertw(log(Pi))) \\ Charles R Greathouse IV, Nov 11 2017

Extensions

More terms from Simon Plouffe

Better name from Jon E. Schoenfield, Dec 30 2014