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TASK #1 - Semiprime
Write a script to generate all Semiprime number <= 100.
For more information about Semiprime, please checkout the wikipedia page
https://en.wikipedia.org/wiki/Semiprime
In mathematics, a semiprime is a natural number that is the product of
exactly two prime numbers. The two primes in the product may equal each
other, so the semiprimes include the squares of prime numbers.
Example
10 is Semiprime as 10 = 2 x 5
15 is Semiprime as 15 = 3 x 5
MY NOTES: Sounds easy, using my existing factors function, and
my existing prime generation code.
TASK #2 - Ulam Sequence
You are given two positive numbers, $u and $v.
Write a script to generate Ulam Sequence having at least 10 Ulam numbers
where $u and $v are the first 2 Ulam numbers.
For more information about Ulam Sequence, please checkout the website
https://en.wikipedia.org/wiki/Ulam_number
The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with U1 =
1 and U2 = 2. Then for n > 2, Un is defined to be the smallest integer
that is the sum of two distinct earlier terms in exactly one way and
larger than all earlier terms.
Example 1
Input: $u = 1, $v = 2
Output: 1, 2, 3, 4, 6, 8, 11, 13, 16, 18
Example 2
Input: $u = 2, $v = 3
Output: 2, 3, 5, 7, 8, 9, 13, 14, 18, 19
Example 3
Input: $u = 2, $v = 5
Output: 2, 5, 7, 9, 11, 12, 13, 15, 19, 23
MY NOTES: hmm.. sounds relatively straightforward. I'm slightly puzzled
by "in exactly one way", but the wikipedia gives an example that clarifies it.
So presumably we're going to check each distinct pair of earlier terms,
checking whether the sum of that pair is an Ulam number at all, whether it's
greater than the last term we've found, and then pick the smallest of all
such numbers found. Obviously O(N**2) or worse.
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