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34, 68 and 99, for instance, are in the sequence because we have the patterns:
......1156.......=34^2............4624......=68^2............9801......=99^2
.....111556......=334^2..........446224.....=668^2..........998001.....=999^2
....11115556.....=3334^2........44462224....=6668^2........99980001....=9999^2
...1111155556....=33334^2......4444622224...=66668^2......9999800001...=99999^2
..111111555556...=333334^2....444446222224..=666668^2....999998000001..=999999^2
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