Intersection between OEIS-A050808 and OEIS-A080053

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Is there any result on the intersection between A050808 and A080053:

OEIS-A080053 = 1, 2, 4, 5, 6, 10,... (Exp(n) is further from an integer than any previous exp(k))

OEIS-A050808 = 1, 2, 18, 50, 127,... (Numbers n such that floor(exp(n)) is prime)

From the entry tables at OEIS this intersection includes only 1 and 2.

I would be interested if there are any larger numbers, which belong to both sequences, or if there might be even infinitely many belonging to both sequences.

Does maybe anyone have information on that issue?

Thanks.