query: Period as a function of n
positive_passages.docid: 111822
positive_passages.text: Is it true that the Fibonacci sequence has the remainders when divided by 3 repeating?
negative_passages.docid: 142067
negative_passages.text: Codomain of a function
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 144601
negative_passages.text: Given $f(x+T) = f(x) + a$, prove that $f(x) = \varphi(x) + {a \over T}x$, where $\varphi(x)$ is periodic with period $T$
negative_passages.docid: 43327
negative_passages.text: convoluted recurrence: $f(2n)=f(n)+f(n+1)+n, f(2n+1)=f(n)+f(n-1)+1$
negative_passages.docid: 104209
negative_passages.text: Functional equation - Cyclic Substitutions
negative_passages.docid: 54297
negative_passages.text: Is $f(x)=10$ a periodic function?
negative_passages.docid: 103285
negative_passages.text: Limit of a periodic function
negative_passages.docid: 43907
negative_passages.text: Contraction mapping in the context of $f(x_n)=x_{n+1}$.
negative_passages.docid: 139092
negative_passages.text: Taking averages at certain intervals
negative_passages.docid: 623
negative_passages.text: variation of a function over countable intervals
negative_passages.docid: 127953
negative_passages.text: Integral of periodic function over the length of the period is the same everywhere
negative_passages.docid: 11806
negative_passages.text: Functional equation.
negative_passages.docid: 78471
negative_passages.text: Closure of $\{\frac{1}{n}\}:=M$
negative_passages.docid: 158230
negative_passages.text: prove that a non constant periodic, continuous function has a "smallest period"
negative_passages.docid: 53713
negative_passages.text: Accumulation Points for $S = \{(-1)^n + \frac1n \mid n \in \mathbb{N}\}$
negative_passages.docid: 158077
negative_passages.text: There should be a space between the period and the N