A328907 Decimal expansion of the solution x = 0.6009668516... to 1 + 3^x = 6^x.

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

Offset: 0

Author

M. F. Hasler, Nov 11 2019

Keywords

• nonn
• cons

Examples

			0.6009668516136754857157052646318381206772279921330513588502639401916921204...
		

Crossrefs

Cf. A329337 (continued fraction).

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), A328906 (1 + 2^x = 6^x).

Programs

Mathematica

RealDigits[x /. FindRoot[1 + 3^x == 6^x, {x, 1}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Jun 28 2023 *)

PARI

print(c=solve(x=0,1, 1+3^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