A356562 Decimal expansion of the unique positive real root of the equation x^x^x = x^x + 1.

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

Offset: 1

Author

Marco Ripà, Aug 12 2022

Keywords

• cons
• nonn

Comments

This constant is case m=2 in a family of real roots of x^^(m+1) - x^^m = 1, where ^^ is tetration. These roots have lim_{m->inf} x(m) = e^(1/e) (see A073229).

Examples

			1.67129219798893255...
		

Crossrefs

Cf. A073229, A124930 (m=1).

Programs

Mathematica

RealDigits[x /. FindRoot[x^(x^x) == x^x + 1, {x, 2}, WorkingPrecision -> 100]][[1]] (* Amiram Eldar, Aug 13 2022 *)

PARI

solve(x=1, 2, x^x^x - x^x - 1) \\ Michel Marcus, Aug 13 2022