The pattern of these numbers is the square numbers. Therefore, following 42 = 16 comes 52 = 25, 62 = 36, 72 = 49.
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It appears as if the pattern is doubling, therefore the next three numbers are 16, 32, and 64.
Should there be a 16 in there somewhere? If so next three are 36, 49 and 64...
12, 13, 16 Add three, then add 1, then add three, then add 1, and so on so forth
Seems like each number is obtained by adding 3 to the previous number. Hence the next three numbers are 13, 16, 19
25 36 49 64 81 100 121 144