A328913 Continued fraction expansion of A328900 = 1.50712659... solution to 2^x + 3^x = 4^x.

1, 1, 1, 34, 1, 1, 2, 1, 1, 1, 2, 3, 28, 2, 1, 1, 2, 4, 3, 2, 7, 2, 35, 3, 1, 1, 2, 1, 2, 53, 1, 33, 1, 1, 1, 2, 2, 2, 35, 10, 52, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 1, 1, 18, 1, 1, 7, 2, 14, 2, 84, 1, 4, 5, 3, 2, 3, 1, 2, 2, 1, 2, 40, 1, 3, 5

Offset: 0

Author

M. F. Hasler, Oct 31 2019

Keywords

• nonn
• cofr

Comments

This number is also the solution to 1 + 1.5^x = 2^x or 1/(1 - 2^-x) = 1 + 2^-x + 3^-x, see A328900.

Examples

			A328900 = 1.50712659... = 1 + 1/(1 + 1/(1 + 1/(34 + 1/(1 + 1/(1 + 1/(2 + ...))))))
		

Crossrefs

Cf. A328900, A328912 (if 3 is replaced by 1).

Programs

Mathematica

ContinuedFraction[ x /. FindRoot[2^x + 3^x == 4^x, {x, 1.5}, WorkingPrecision -> 100]] (* Robert G. Wilson v, Nov 12 2019 *)

PARI

contfrac(solve(s=1,2,1+1.5^s-2^s)) \\ Use e.g. \p999 to get more terms.