The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002823 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002823

Number of period-n solutions to a certain "universal" equation related to transformations on the unit interval.
(history; published version)

#24 by Jon E. Schoenfield at Sat Jan 29 01:01:07 EST 2022

STATUS

editing

approved

#23 by Jon E. Schoenfield at Sat Jan 29 01:01:05 EST 2022

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#22 by M. F. Hasler at Wed Nov 05 14:27:44 EST 2014

STATUS

proposed

approved

#21 by M. F. Hasler at Wed Nov 05 14:27:39 EST 2014

STATUS

editing

proposed

#20 by M. F. Hasler at Wed Nov 05 14:19:58 EST 2014

CROSSREFS

Cf. A000048, A001372.

STATUS

approved

editing

#19 by N. J. A. Sloane at Wed Nov 05 11:03:22 EST 2014

STATUS

proposed

approved

#18 by M. F. Hasler at Wed Nov 05 10:01:36 EST 2014

STATUS

editing

proposed

#17 by M. F. Hasler at Wed Nov 05 09:59:58 EST 2014

COMMENTS

a(n) <= A000048(n), since the solutions counted here are a subset of the solutions counted by A000048 (called U sequence in the paper). The observed equality for prime n means that there are in that this case no harmonics , which would "coalesce" with their fundamentalsdisappear. - M. F. Hasler, Nov 05 2014

Discussion

Wed Nov 05

10:01

M. F. Hasler: Added some more verbosity.

#16 by M. F. Hasler at Wed Nov 05 09:58:27 EST 2014

COMMENTS

a(n) <= A000048(n), with since the solutions counted here are a subset of the solutions counted by A000048 (called U sequence in the paper). The observed equality for prime n. (Conjectured means that there are in that case no harmonics which would "coalesce" with their fundamentals.) - M. F. Hasler, Nov 05 2014

STATUS

proposed

editing

#15 by M. F. Hasler at Wed Nov 05 08:29:54 EST 2014

STATUS

editing

proposed

Discussion

Wed Nov 05

09:24

Charles R Greathouse IV: Is the whole statement conjectural, or just one of the parts?

09:35

M. F. Hasler: If I understand the paper correctly, the first part is not conjectural, the solutions to (4.1) with (6.2) [counted here] are a subset of those corresponding to A48 (what he calles U sequence). I'm not yet sure whether what he calls "harmonics" is really related to the compositeness of k, which would make the second part also true. (No "harmonics" for prime k would yield equality.)