Is it Possible to Create a Sequence That Visits 0, 1, and 5 Infinitely Often?

[adrivit]

Construct a sequence that visits the numbers 0,1,5 infinitely often.?
A sequence Sn visits a number A when for infinitely many n in N, Sn = A. Example: The sequence (-1)^n visits -1 and 1 infinitely.

 

[hamster143]

n mod 6?

 

[dodo]

(3^n - 1) mod 7?

 

[hamster143]

or even ((n mod 3)+5)mod 6.

 

[dodo]

Or (11^n mod 37) mod 6.

 

[CRGreathouse]

0,-1,1,0,-1,1,-2,2,0,-1,1,-2,2,-3,3,0,-1,1,-2,2,-3,3,-4,4,... visits all integers infinitely often.

 

[hamster143]

$$2 - (cos(2\pi n/3) + cos(4\pi n/3)) - (2/\sqrt{3})(sin(2\pi n/3) - sin(4\pi n/3))$$

 

[dodo]

$$\sum_{k=1}^n a_k \, , \quad \mbox{where } a_k \mbox{ is the recurrence sequence given by}$$

$$\begin{align*} a_1 &= 1 \\ a_2 &= 4 \\ a_k &= -a_{k-1}-a_{k-2} \, , \quad \scriptstyle{k \ge 3} \end{align*}$$

 

[hamster143]

$$\left\lfloor(50/333)*10^n\right\rfloor mod 10$$

 

[ramsey2879]

$$\sum_{k=1}^n a_k \, , \quad \mbox{where } a_k \mbox{ is the recurrence sequence given by}$$

$$\begin{align*} a_1 &= 1 \\ a_2 &= 4 \\ a_k &= -a_{k-1}-a_{k-2} \, , \quad \scriptstyle{k \ge 3} \end{align*}$$

This sequence doesn't contain even one zero. There must be a typo or something! Oh! I get It Sum 1,4,-5 = 0 etc/