When approaching this question, it is best to do the first ten numbers, record them and then branch out on the different possibilities, eliminating them one by one. It is also best to try all of the ones in between in case the correct numbers are just a subset. It is also good to do very large numbers because they are more likely to differentiate subsets from the actual solution.
Blue: The last digit has to be 4 or 9. Examples tested:4,9,14,19,24,29,34,39,44,49,54,1247594etc.Examples that did not work:1,2,3,5,6,7,8,10,4367,8745,465,43,5547675,9898,987,61,32542,etc.
Red: Multiples of 8. Examples tested: 8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,88136 etc.Examples that did not work:1,2,3,4,5,6,7,9,10,5465667,7889,1111233,45567890009889,etc.
Green: Multiples of 11 with an further addition of 7/subtraction of 4. Examples tested: 7,18,29,40,51,62,73,84,95,106,117,128,139,150,620811143etc. Examples that did not work:1,2,3,4,5,6,8,9,4354533,5364566767,647645,65365665,etc
Yellow: Multiples of 6 with a further addition of 4.Examples tested:Examples tested: 10,16,22,28,34,,40,46,52,58,64,278717212,etc.Examples that did not work:1,2,3,4,5,6,7,8,9,45,57,278717213.