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Decimal expansion of the solution of 1/x^3 + 1/3^x = 1.
3

%I #8 Jul 11 2020 07:37:03

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

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

%U 9,5,1,0,1,3,8,1,2,8,8,0,2,9,9,7,4,8

%N Decimal expansion of the solution of 1/x^3 + 1/3^x = 1.

%F x^3 + 3^x = x^3 * 3^x.

%e x = 1.12177497902956545655218...

%t r = x /. FindRoot[1/x^3 + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]

%t RealDigits[r][[1]] (* A329995 *)

%t Plot[1/x^2 + 1/2^x - 1, {x, 1, 2}]

%o (PARI) solve(x=1, 2, 1/x^3 + 1/3^x - 1) \\ _Michel Marcus_, Jul 11 2020

%Y Cf. A329996, A329997.

%K nonn,cons,easy

%O 1,3

%A _Clark Kimberling_, Jan 03 2020