%I #12 Jun 28 2023 08:21:37

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

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

%U 5,6,2,8,2,5,5,8,6,6,8,4,4,8,2,3,5,0,9,7,2,4,0,4,3,3,9,0,0,5,0

%N Decimal expansion of the solution x = 0.4895363211996... to 1 + 2^x = 6^x.

%e 0.489536321199649488689875316822650189403586515771912127846436678619255628...

%t RealDigits[x /. FindRoot[1 + 2^x == 6^x, {x, 1}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Jun 28 2023 *)

%o (PARI) print(c=solve(x=0,1, 1+2^x-6^x)); digits(c\.1^default(realprecision))[^-1] \\ [^-1] to discard possibly incorrect last digit. Use e.g. \p999 to get more digits. - _M. F. Hasler_, Oct 31 2019

%Y Cf. A329336 (continued fraction).

%Y Cf. A242208 (1 + 2^x = 4^x), A328900 (2^x + 3^x = 4^x), A328904 (1 + 3^x = 5^x), A328905 (1 + 2^x = 5^x), A328907 (1 + 3^x = 6^x).

%K nonn,cons

%O 0,1

%A _M. F. Hasler_, Nov 11 2019