A309211 -id:A309211 - cp's OEIS frontend

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

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

A309208 Decimal expansion of (3 tanh (3 tanh (3 tanh (...))))^(-2).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 29 2019

This is the decimal expansion of 1/x^2 where x is the constant defined in A309211.

			.1122528288730582219511299311388265401208...

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. A309207, A309211.

More terms from Daniel Suteu, Jul 30 2019

A359809 Decimal expansion of the positive solution to tanh(x) = x/2.

Original entry on oeis.org

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

Offset: 1

M. F. Hasler, Jan 13 2023

Also, point where e^-(x/2 - 1)^2 + e^-(x/2 + 1)^2 has its maximum.

			1.91500804815453748135300306100481565...

Cf. A309211.

RealDigits[x /. FindRoot[Tanh[x] == x/2, {x, 2}, WorkingPrecision -> 110], 10, 105][[1]] (* Amiram Eldar, Jan 13 2023 *)

localprec(199); digits(solve(x=1,2,tanh(x)-x/2)\.1^150)

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A309208 Decimal expansion of (3 tanh (3 tanh (3 tanh (...))))^(-2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A359809 Decimal expansion of the positive solution to tanh(x) = x/2.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI