A329337 Continued fraction of A328907 = 0.6009668516..., solution to 1 + 3^x = 6^x.

0, 1, 1, 1, 1, 40, 1, 3, 2, 1, 2, 23, 1, 13, 1, 8, 1, 15, 2, 3, 103, 4, 10, 4, 2, 2, 2, 1, 1, 84, 1, 4, 1, 3, 1, 1, 5, 1, 7, 23, 8, 1, 8, 24, 1, 1, 2, 12, 39, 14, 19, 3, 4, 8, 3, 2, 1, 4, 1, 8, 1, 1, 1, 2, 1, 10, 1, 35, 1, 10, 2, 2, 2, 1, 1, 15, 2, 3, 1, 4, 7, 5, 1, 9, 1, 1, 1, 1, 2, 3, 3, 2, 1, 4, 54, 4, 1, 3, 2, 1, 1, 1, 1, 4, 22, 1, 4, 3, 1, 1, 1, 2, 6, 1, 1, 4, 1, 8, 1, 20

Offset

0,6

Links

Table of n, a(n) for n=0..119.

Example

0.6009668516... = 0 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(40 + 1/(1 + 1/(3 + ...)))))))

Mathematica

ContinuedFraction[x/.FindRoot[1+3^x==6^x, {x, 1}, WorkingPrecision->150]] (* Harvey P. Dale, Jun 13 2022 *)

Prog

(PARI) contfrac(c=solve(x=0, 1, 1+3^x-6^x))[^-1] \\ discarding possibly incorrect last term. Use e.g. \p999 to get more terms. - M. F. Hasler, Oct 31 2019

Crossrefs

Cf. A328912 (cont. frac. of A242208: 1 + 2^x = 4^x), A328913 (cont. frac. of A328900: 2^x + 3^x = 4^x), A329335 (cont. frac. of A328905: 1 + 2^x = 5^x).

Sequence in context: A013420 A156917 A176644 * A078084 A037937 A126652

Adjacent sequences: A329334 A329335 A329336 * A329338 A329339 A329340

Keyword

nonn,cofr

Author

M. F. Hasler, Nov 11 2019

Status

approved