%I #33 Aug 22 2022 22:16:14
%S 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,
%T 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,
%U 1,7,7,3,9,6,0,2,3,3,6,4,9,0,6,4,2,6,9
%N Decimal expansion of the unique positive real root of the equation x^x^x = x^x + 1.
%C 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).
%e 1.67129219798893255...
%t RealDigits[x /. FindRoot[x^(x^x) == x^x + 1, {x, 2}, WorkingPrecision -> 100]][[1]] (* _Amiram Eldar_, Aug 13 2022 *)
%o (PARI) solve(x=1, 2, x^x^x - x^x - 1) \\ _Michel Marcus_, Aug 13 2022
%Y Cf. A073229, A124930 (m=1).
%K cons,nonn
%O 1,2
%A _Marco RipĂ _, Aug 12 2022