I think the first-known matching pattern plays a huge role. The original 2,4,8 sequence, for example, locked me in immediately to doubles of the previous number (causing me to test 1,2,4 and 7,14,28 and such). Had it been a different starting sequence (like 3,9,27), I might've based my guesses differently. Same for 1,2,3.

In other words, first impressions really are important.