ln(m)'s close to integers

[Don Reble]

> Consider the integers m, m >= 2, such that:
> ln(m) is closer to an integer than any previous term of the sequence.

	You must mean "...than any previous logarithm of the sequence."
	Therefore:
2 3 7 20 148 403 1096 1097 2980 2981 8103 59874 162755 442413 1202604
3269017 8886110 8886111 24154952 24154953 65659969 178482301 3584912846
9744803446 26489122130 72004899337 195729609428 195729609429
532048240602 1446257064291 3931334297144 78962960182680 ...

> I would guess that the sequence would contain consecutive terms,
> sometimes, which are close to the SAME integer.
	Yep: 2 3; 1096 1097; 2980 2981; etc.

> But almost anything about this sequence (such as its actual terms) is
> unknown to me at this time.
	For one thing, it's related to A000149 and A001671.
	And maybe A004790.
--
Don Reble       djr at nk.ca