A309208 -id:A309208 - cp's OEIS frontend

A309211 Decimal expansion of a solution to x = 3*tanh(x).

2, 9, 8, 4, 7, 0, 4, 5, 8, 5, 3, 5, 7, 8, 8, 6, 8, 1, 5, 5, 5, 9, 7, 9, 1, 2, 3, 4, 6, 1, 5, 6, 4, 3, 1, 6, 4, 4, 8, 5, 3, 9, 7, 0, 6, 9, 1, 2, 3, 8, 4, 4, 2, 6, 0, 4, 9, 7, 0, 6, 1, 5, 6, 9, 4, 0, 9, 9, 8, 0, 5, 7, 3, 3, 3, 9, 9, 6, 7, 9, 4, 2, 0, 6, 8, 3, 3, 9, 7, 9, 3, 3, 8, 3, 1, 7, 9, 4, 4, 5, 6, 4, 2, 8, 5, 8

Offset: 1

N. J. A. Sloane, Jul 30 2019

			2.9847045853578868155597912346...

Cf. A309207 (continued fraction expansion), A309208.

Digits := 120 ; fsolve(x=3*tanh(x),x,0..10.) ; # R. J. Mathar, Jul 30 2019

RealDigits[x/.FindRoot[x==3Tanh[x],{x,3},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Jul 30 2019 *)

A309211_first(n)={localprec(n\.9+9);digits(solve(x=2.9,3,tanh(x)*3-x)\10^(1-n))} \\ M. F. Hasler, Jan 27 2023

More terms from Daniel Suteu, Jul 30 2019

A309207 Continued fraction expansion of (3 tanh (3 tanh (3 tanh (...)))).

Original entry on oeis.org

2, 1, 64, 2, 1, 1, 1, 3, 4, 1, 2, 3, 1, 272213, 1, 2, 1, 16, 110, 4, 4, 4, 1, 1, 1, 4, 1, 1, 916, 21, 11, 6, 2, 2, 2, 1, 2, 16, 3, 1, 1, 2, 2, 9, 1, 2, 8, 2, 4, 3, 2, 2, 1, 9, 6, 5, 3, 1, 4, 2, 12, 17, 1, 3, 1, 3, 1, 1, 3, 1, 7, 1, 1, 2, 8, 2, 1, 1, 5, 11, 90, 1

Offset: 0

N. J. A. Sloane, Jul 29 2019

This is the continued fraction expansion of the constant defined in A309211.

W. M. Gosper, Material from Bill Gosper's Computers & Math talk, M.I.T., 1989, i+38+1 pages, annotated and scanned, included with the author's permission. (There are many blank pages because about half of the original pages were two-sided, half were one-sided.)

Cf. A309208, A309211.

ContinuedFraction[Reduce[x == 3 Tanh@x, x, Reals][[3, 2]], 33] (* Bill Gosper, Jul 30 2019 *)

More terms from Daniel Suteu, Jul 30 2019

cp's OEIS Frontend

A309211 Decimal expansion of a solution to x = 3*tanh(x).

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