The definition similar to this except that it reaches 2 is simply 1, 2, 3, 6.
Table of n, a(n) for n=1..13.
11 does not qualify for the term after 10 because the sum of the reciprocals of the first 11 terms would then fall between 3.01 and 3.02.
Sequence in context: A117923 A117924 A200373 * A004839 A032993 A081385
Adjacent sequences: A140332 A140333 A140334 * A140336 A140337 A140338
J. Lowell, Jul 21 2008