A197834 - OEIS

Draft edits for A197834

(Bold, blue-underlined text is an ; faded, red-underlined text is a ~~deletion~~.)

A197834

Decimal expansion of the maximum of (cos(x))^2+(sin(3*Pi*x))^2.
(history; published version)

Individual edits:

#6 by Charles R Greathouse IV at Wed Jul 22 16:09:54 EDT 2026

EXAMPLE

x=1.9727766369395095624370979608845877218621869...

PROG

STATUS

approved

Discussion

Wed Jul 22

16:11

Charles R Greathouse IV: At x = -3.16638764..., the function is 1.9993784... and so this cannot be a maximum. If my program is correct the latter should be the value for this sequence, but even if not, the existing terms are wrong.

16:11

Charles R Greathouse IV: Additionally, the offset should be 1 if I understand correctly.

#7 by Charles R Greathouse IV at Wed Jul 22 16:11:39 EDT 2026

STATUS

editing

Discussion

Wed Jul 22

16:27

Amiram Eldar: Looking at the code for this constant, that is annoyingly written in A197833, at the 3rd line there is "{x, .16, .17}", which means that the author assumed that the location of the maximum is between 0.16 and 0.17. So the data is for a local maximum at x = 0.1648..., and thus it is indeed wrong (and the offset should be indeed 1).

#8 by Robert C. Lyons at Wed Jul 22 19:27:13 EDT 2026

MATHEMATICA

(See the program at A197833.)

STATUS

proposed

#9 by Charles R Greathouse IV at Wed Jul 22 21:09:01 EDT 2026

DATA

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

OFFSET

0,2

EXAMPLE

1.9727766369395095624370979608845877218621869...

MATHEMATICA

(* See the program at A197833. *)

EXTENSIONS

Discussion

Wed Jul 22

21:09

Charles R Greathouse IV: If there is a different/better way to correct this please let me know.

#10 by Charles R Greathouse IV at Wed Jul 22 21:09:21 EDT 2026

STATUS

editing

All edits since published version (omitting small deletions for readability):

NAME

Decimal expansion of the maximum of (cos(x))^2+(sin(3*Pi*x))^2.

DATA

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

OFFSET

0,2

COMMENTS

For a discussion and guide to related sequences, see A197739.

EXAMPLE

x=1.9727766369395095624370979608845877218621869...

MATHEMATICA

(See the program at A197833.)

PROG

CROSSREFS

Cf. A197739, A197833.

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 19 2011

EXTENSIONS

STATUS

approved

Discussion

Wed Jul 22

16:11

Charles R Greathouse IV: At x = -3.16638764..., the function is 1.9993784... and so this cannot be a maximum. If my program is correct the latter should be the value for this sequence, but even if not, the existing terms are wrong.

16:11

Charles R Greathouse IV: Additionally, the offset should be 1 if I understand correctly.

16:27

Amiram Eldar: Looking at the code for this constant, that is annoyingly written in A197833, at the 3rd line there is "{x, .16, .17}", which means that the author assumed that the location of the maximum is between 0.16 and 0.17. So the data is for a local maximum at x = 0.1648..., and thus it is indeed wrong (and the offset should be indeed 1).

21:09

Charles R Greathouse IV: If there is a different/better way to correct this please let me know.