A329336 Continued fraction of A328906 = 0.4895363211996..., solution to 1 + 2^x = 6^x.

0, 2, 23, 2, 1, 1, 4, 1, 1, 27, 4, 12, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 2, 6, 1, 10, 4, 3, 4, 1, 2, 1, 1, 43, 69, 1, 2, 41, 1, 3, 2, 3, 3, 1, 5, 4, 1, 1, 1, 7, 1, 1, 1, 11, 13, 2, 3, 1, 1, 1, 118, 2, 1, 1, 12, 1, 2, 2, 2, 6, 2, 3, 1, 4, 1, 8, 1, 1, 18, 2, 21, 1, 4, 1, 3, 1, 51, 6, 1, 1, 18, 2, 1, 1, 2, 56, 1, 1, 5, 4, 1, 4, 7, 1, 2, 2, 1, 9, 76, 2, 1, 3, 1, 5, 3, 1, 7, 6

Offset

0,2

Links

Table of n, a(n) for n=0..126.

Example

0.4895363211996... = 0 + 1/(2 + 1/(23 + 1/(2 + 1/(1 + 1/(1 + 1/(4 + 1/...))))))

Mathematica

ContinuedFraction[x/.FindRoot[1+2^x==6^x, {x, .4}, WorkingPrecision->1000], 150] (* Harvey P. Dale, Oct 15 2022 *)

Prog

(PARI) contfrac(c=solve(x=0, 1, 1+2^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), A329334 (cont. frac. of A328904: 1 + 3^x = 5^x).

Sequence in context: A261198 A052077 A124604 * A323396 A359272 A107801

Adjacent sequences: A329333 A329334 A329335 * A329337 A329338 A329339

Keyword

nonn,cofr

Author

M. F. Hasler, Nov 11 2019

Status

approved