A392320 Indices of nonzero entries in the continued hyperbolic-tangent expansion of Pi.

0, 73, 166, 207, 213, 216, 595, 986, 1069, 1075, 1117, 1118, 1135, 1369, 1383, 1397, 1422, 3986, 4040, 4041, 4042, 4043, 4075, 4083, 4476, 4501, 8497, 31301, 31304, 56570, 60320, 62888, 63025, 63573, 63600

Offset

1,2

Comments

Pi = 3 + tanh(x(0) + tanh(x(1) + tanh(x(2) + tanh(x(3) + ...)))). The set {x(k)} is sparse, so k is in this sequence only when x(k) is nonzero.

Links

Table of n, a(n) for n=1..35.

Patrick J. Millican, contfunc GitHub repository.

A. Rényi, Representations for real numbers and their ergodic properties, Acta Mathematica Academiae Scientiarum Hungaricae 8, 477-493 (1957).

Mathematica

ContTanh[n_, mx_] := Block[{k = 0, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = ArcTanh[x - s]; If[s > 0, AppendTo[lst, k] ]; k++]; lst]; ContTanh[Pi, 100000]

Crossrefs

Cf. A000796.

Sequence in context: A071844 A078856 A142326 * A142377 A389206 A044405

Adjacent sequences: A392317 A392318 A392319 * A392321 A392322 A392323

Keyword

nonn,more

Author

Patrick J. Millican, Mar 31 2026

Status

approved