Araris Valerian Posted July 17, 2017 Report Share Posted July 17, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
18th Shard Posted July 19, 2017 Report Share Posted July 19, 2017 Perhaps insert a term which results as 0 when x is odd/even? Ex. y= x^2 + 1 + x*([x+1]mod 2) 0 Quote Link to comment Share on other sites More sharing options...
Lucky MOPper Posted February 7, 2020 Report Share Posted February 7, 2020 Use (-1)^x+1? 0 Quote Link to comment Share on other sites More sharing options...
Truthwatcher Artifabrian Posted April 4, 2022 Report Share Posted April 4, 2022 It looks like your function is equivalent to this image. Perhaps your set of functions is just polynomials plus that extra term at the end? 0 Quote Link to comment Share on other sites More sharing options...
Frustration Posted April 4, 2022 Report Share Posted April 4, 2022 8 hours ago, Truthwatcher Artifabrian said: It looks like your function is equivalent to this image. Perhaps your set of functions is just polynomials plus that extra term at the end? This thread has been dead for two years. 0 Quote Link to comment Share on other sites More sharing options...
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