Can a Sequence Visit 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.

 

[HallsofIvy]

What's wrong with a_3n= 0, a_3n+1= 1, a_3n+2= 5 for all n?

 

[adrivit]

But, the function doesn't visit 0,1,5 infinitely many times here does it?

 

[adrivit]

I'm sorry, I misunderstood. Thanks for the solution!

 

[adrivit]

How about the sequence which visits all N infinitely?

 

[Office_Shredder]

Do you have any ideas? There is one that is fairly similar to the one that visits 0,1 and 5 infinitely often

 

[adrivit]

I was wondering whether N mod N would do the trick. Or maybe considering the field R^inf and the sub field N inside that. But I am not sure of either.