Blue smoke no code

[crosbyfd85]

Just purchased an 05 f250 fx4 king ranch 2 weeks ago, in the first week it would randomly drain the battery so I checked the batteries and they were good but I was told the alternator needed to be replaced, did that and the night I replaced it I had the same issue, it did it once last weekend and hasn't done it since, the mechanic that installed it can't figure out y that happened.

Now I'm noticing blue smoke when I start it, it clears out after I drive it a few miles, it has done this since the day I got it, I'm not thinking a check engine light so I'm assuming it's not the injectors, Im having a cold air intake and EGR bypass installed next week to solve my problem with 9mpg should I worry about the smoke?

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