Exercise from math circle

periodicity_modulo.R

# https://stats.stackexchange.com/a/1214/1381
find.freq <- function(x)
{
  n <- length(x)
  spec <- spec.ar(c(x),plot=FALSE)
  if(max(spec$spec)>10) # Arbitrary threshold chosen by trial and error.
  {
    period <- round(1/spec$freq[which.max(spec$spec)])
    if(period==Inf) # Find next local maximum
    {
      j <- which(diff(spec$spec)>0)
      if(length(j)>0)
      {
        nextmax <- j[1] + which.max(spec$spec[j[1]:500])
        period <- round(1/spec$freq[nextmax])
      }
      else
        period <- 1
    }
  }
  else
    period <- 1
  return(period)
}

n <- 0:10
y <- x%%7
x <- 2^n
x%%13

n <- 0:200
x <- 2^n
# primes <- randtoolbox::get.primes(n = 10)
primes <- c(2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
period <- vector(length = length(primes))
for (i in 1:length(primes)){
  prime <- primes[i]
  period[i] <- find.freq(x%%prime)
}


plot(primes, period)