the sequence really is insane :) , as 347 is prime I dont think there exists a valid progression and there is no nice interval. Did you try converting these to different different bases?
i figure out that all numbers which where consisted of 2 digits the made into numbers of 3 digits: 39 43 47 51 55 59 63 67 71 75 79 83
394 347 515 559 636 771 757 983
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