infinite loop - Computation R program

Question

I want to compute the smallest possible number that is divisible evenly by all the natural numbers from 1-20; I have written the following program in R and am not getting the desired output (rather it seems my loop is almost never ending).

My program is as follows:

a = 21
c = 0
while ( c < 20){
    c = 0
    n = 1
    while ( n < 21 ){
        if (a%%n == 0) c = c + 1
        n = n+1
    }
    a = a + 1
}
print (a)

Where did I go wrong?

Answer 1

Here's a more R-like solution using that fact that the answer will be the product of primes, p <= 20, each raised to an index i such that p^i <=20

sMult <- function(x)
# calculates smallest number that 1:x divides
{
    v <- 1:x
    require(gmp) # for isprime
    primes <- v[as.logical(isprime(v))]
    index <- floor(log(x)/log(primes))
    prod(rep(primes,index))
}

Which yields:

> sMult(20)
[1] 232792560
> sMult(20)%%1:20
 [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

While this solution is general, it should be noted that for large x, isprime is probabalistic. Of course, when this is likely to give false results, you are also likely to have a number so large that it will not be able to be stored accurately. Fortunately the gmp package implements a large integer class, bigz. To use this change to final line of the function to:

prod(as.bigz(rep(primes,index)))

Compare the following results:

> sMult(1000)
[1] Inf
> sMult2(1000)
[1] "7128865274665093053166384155714272920668358861885893040452001991154324087581111499476444151913871586911717817019575256512980264067621009251465871004305131072686268143200196609974862745937188343705015434452523739745298963145674982128236956232823794011068809262317708861979540791247754558049326475737829923352751796735248042463638051137034331214781746850878453485678021888075373249921995672056932029099390891687487672697950931603520000"