Is there a simple function that generates the series; 1,1,2,1,1,2,1,1,2…1,1,2,1,1,2,1,1,2… or −1,−1,1,−1,−1,1…-1,-1,1,-1,-1,1… [closed]

I’m thinking about this question in the sense that we often have a term (1)n for an integer n, so that we get a sequence 1,1,1,1… but I’m trying to find an expression that only gives every 3rd term as positive, thus it would read;
1,1,1,1,1,1,1,1…

Alternatively a sequence yielding 1,1,2,1,1,2,1,1,2… could also work, as n could just be substituted by it in (1)n

Answer

Let F_n be the Fibonacci sequence 0,1,1,2,3,5,8,13,21,34,… then a possible sequence is (-1)^{F_{n+1}}

Attribution
Source : Link , Question Author : Kristaps John Balodis , Answer Author : Community

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