A328905 Decimal expansion of the solution x = 0.56389552425993647949... to 1 + 2^x = 5^x.

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

Offset: 0

Author

M. F. Hasler, Oct 31 2019

Keywords

• nonn
• cons

Examples

			0.5638955242599364794903929459379565655152117305099552985928083801204662005228...
		

Crossrefs

Cf. A329334 (continued fraction).

Cf. A242208 (1 + 2^x = 4^x), A328900 (2^x + 3^x = 4^x), A328904 (1 + 3^x = 5^x).

Programs

Mathematica

RealDigits[x /. FindRoot[1 + 2^x == 5^x, {x, 1}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Jun 28 2023 *)

PARI

print(c=solve(x=0,1, 1+2^x-5^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