A084305 Continued fraction expansion of tanh(tanh(1)).

0, 1, 1, 1, 3, 1, 5, 3, 1, 2, 85, 1, 2, 2, 2, 1, 1, 1, 2, 5, 1, 7, 1, 1, 4, 1, 4, 1, 1, 1, 1, 6, 3, 1, 3, 3, 2, 1, 9, 12, 16, 4, 1, 1, 1, 2, 1, 2, 1, 49, 3, 7, 1, 2, 6, 1, 1, 1, 6, 1, 3, 2, 1, 1, 5, 2, 1, 199, 8, 1, 8, 1, 1, 2, 2, 1, 9, 1, 4, 4, 4, 2, 2, 1, 2, 1, 3, 1, 249, 1, 2, 2, 1, 1, 4, 1, 1, 135, 3, 2, 1

Offset: 0

Author

Labos Elemer, Jun 04 2003

Keywords

• cofr
• easy
• nonn

Comments

While the continued fraction of tanh(1) = {0, 1, 3, 5, 7, 11, ..}, i.e., 0 and odd numbers, twice applying tanh() we get this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A083124, A084304.

Programs

Maple

with(numtheory); cfrac(tanh(tanh(tanh(1))),300,'quotients');

Mathematica

ContinuedFraction[Tanh[Tanh[1]],120] (* Harvey P. Dale, Jan 19 2024 *)

PARI

contfrac(tanh(tanh(1))) \\ Amiram Eldar, Mar 08 2025