The Ulam sequence starts with:
ulam = [1, 2]
The next number in the sequence is the smallest positive number that is equal to the sum of 2 distinct numbers (that are already in the sequence) exactly one way. Trivially, this is 3, as there are only 2 numbers in the starting sequence.
ulam = [1, 2, 3]
The next number is 4, which is the sum of 3+1. 4 is also 2+2, but this equation does not count, as the 2 addends have to be distinct.
ulam = [1, 2, 3, 4]
The next number cannot be 5, as 5 = 1 + 4, but also 5 = 2 + 3. There should only be one way to make an Ulam number from 2 distinct addends found in the sequence. The next number is 6 (2+4). There are 2 ways to make 7 (1+6 or 3+4), so the next is 8 (2+6). And so on.
ulam = [1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, …]
Create a function that takes a number n and returns the nth number in the Ulam sequence.
ulam(4) ➞ 4
ulam(9) ➞ 16
ulam(206) ➞ 1856
N/A