21 lines
992 B
R
21 lines
992 B
R
genNStern <- function(n)
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{
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sternNums <- c(1, 1)
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i <- 2
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while((endIndex <- length(sternNums)) < n)
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{
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#To show off R's vectorization, the following line is deliberately terse.
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#It assigns sternNums[i-1]+sternNums[i] to sternNums[endIndex+1]
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#and it assigns sternNums[i], the "considered" number, to sternNums[endIndex+2], now the end of the sequence.
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#Note that we do not have to initialize a big sternNums array to do this.
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#True to the algorithm, the new entries are appended to the end of the old sequence.
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sternNums[endIndex + c(1, 2)] <- c(sum(sternNums[c(i - 1, i)]), sternNums[i])
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i <- i + 1
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}
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sternNums[seq_len(n)]
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}
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#N=5000 was picked arbitrarily. The code runs very fast regardless of this number being much more than we need.
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firstFiveThousandTerms <- genNStern(5000)
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match(1:10, firstFiveThousandTerms)
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match(100, firstFiveThousandTerms)
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all(sapply(1:999, function(i) gmp::gcd(firstFiveThousandTerms[i], firstFiveThousandTerms[i + 1])) == 1)
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