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

0,5

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A083124, A084304.

Sequence in context: A340530 A147754 A360325 * A347066 A099375 A348835

Adjacent sequences: A084302 A084303 A084304 * A084306 A084307 A084308

Keyword

cofr,easy,nonn,changed

Author

Labos Elemer, Jun 04 2003

Status

approved