Dave Smith Instruments SYNTHESIZERS

On Mon, Oct 27, 2003 at 12:51:57PM -0500, Robert Shanks wrote:
>    I think it has
>    something  to do with 16 = 2 * 2 * 2 * 2,  15 = 3 * 5, 14 = 2 * 7, and
>    13 is
>    a  prime,  but  I don't know where to go with it after that.  (ok, you
>    math
>    head help me out here)

you're looking for the least common multiple (LCM). two (common) ways to
find it are:
  1) write down all multiples of each number and see where they coincide
     (which is tedious with this set)
  2) factor each into primes; then for each *different* prime, count how
     many times it appears in each number and take the *greatest* such
     count; then multiply these counts times the primes themselves and you
     have your LCM

so in your case (using method 2) we have:
  - factor into primes (which you did):
    16 = 2 * 2 * 2 * 2
    15 = 5 * 3
    14 = 7 * 2
    13 = 13 * 1 (prime)
  - the greates number of times each prime appears as a factor (in a
    single number) is:
    13 - once
    7  - once (in 14)
    5  - once (in 15)
    3  - once (in 15)
    2  - 4 times (in 16)
  - multiple the prime occurances times the primes themselves
    to get the LCM:
    (13*1) * (7*1) * (5*1) * (3*1) * (2^4) = 21840

>    What I did was write a BASIC program with four
>    non-nest  loops  and  check  for my starting numbers 0, 0, 0, 0.  That
>    told me
>    sequences  of  16,  15,  14,  13  repeats after 21840 ( or half of the
>    straight
>    multiplication  of  all  the numbers.)

hmmm....I'm not sure if that will always be correct. I'd have to see the
code :-)

the longest possible sequence on the Evolver (by the way) is
16, 15, 13, 11; it repeats every 16*15*13*11 = 34320 steps.

thanks for the post! it was a fun way to spend my morning
coffee-drinking time :-)

Joe