Jump to content

Periodic(ish) Polynomial(ish) Functions

Recommended Posts

I've come across a weird class of functions, where the overall growth is polynomial bounded above and below, but there is some periodic behavior. One example is the following sequence of numbers: 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43. The 1st, 3rd, 5th, and so forth entries correspond to the function x^2+1, if x=1 corresponds to the value 2. The other entries correspond to x^2+x+1, if we match x=1 to the entry valued 3.

Has anyone seen functions/sequences like this before? I'm trying to prove that certain sequences always have this sort of periodic polynomial behavior, but I haven't seen these things before, which is making it hard to prove that an infinite set of functions falls into this category.

Link to comment
Share on other sites

  • 2 years later...
  • 2 years later...

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

  • Recently Browsing   0 members

    • No registered users viewing this page.
  • Create New...