[seqfan] "Piecewise periodicity"

[Veikko Pohjola]

Dear seqfans,

The roots of equation floor(tan(n))=1 have interesting features many of which, I think, would deserve a place in OEIS. Nice sequences, besides the roots themselves, follow from the peculiar ”piecewise periodicity" of each root. By ”peculiar” I refer to the phenomenon that the roots having the period, characteristic to the root in question, form subsequences (”pieces”) which follow each other with a phase shift such that the original phase is reached again after a higher-level period. The latter has again its own period and so on. 

If translated to musical terms, all this results in a myriad of non-ending, continuously varying polyrhythmic compositions.

The symmetry of the first differences of the roots results in an ever-increasing palindrome shifting its position within the sequence of the roots, as the function of n. The growth of palindrome as well as its shift also form nice sequences.

I plan to submit some of these.