Questions tagged [sequences-and-series]

For questions concerning sequences and series. Typical questions concern, but are not limited to: recurrence relations, convergence tests, identifying sequences, identifying terms. For questions on finite sums, use the (summation) tag instead.

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Prime number and Relationship of Sequences of period 4,5,and 6

Let $p$ be a prime number.($p \neq 2,3,5$) Let $t^+,t^-,a$ be sequences. $t^+_{k+5}=t^+_k,t^+_1=0,t^+_2=-1,t^+_3=-1,t^+_4=0,t^+_5=2$ $t^-_{k+5}=t^-_k,t^-_1=-1,t^-_2=0,t^-_3=0,t^-_4=-1,t^-_5=2$ $a_k=...
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Limit associated with a recursion

If $z_n < 2y_n$ then $y_{n+1} = 4y_n - 2z_n$ $z_{n+1} = 2z_n + 3$ Else $y_{n+1} = 4y_n$ $z_{n+1} = 2 z_n - 1$ Consider the following limit: $$\lim_{n\rightarrow\infty} \frac{1}{n}\left(z_{n+1}...