[seqfan] Re: Definition of A052130; question about Beatty sequences.

[David Wilson]

Let f(m, n) = #{ 1 <= k <= 2^m : omega(k) = n } where omega = A001222.

Then a(n) = lim m->inf f(m, m - n).

So really, a(n) is the limiting value as m increases.

Perhaps it should read "for sufficient m" instead of "for very large m".

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of L. Edson Jeffery
Sent: Saturday, April 04, 2015 10:24 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Definition of A052130; question about Beatty sequences.

Can someone please explain why the condition "For m very large" is required in the definition (%N) of A052130 (https://oeis.org/A052130)?

For adjacent terms in a Beatty sequence, are there always only two distinct first differences, and is there a formula for determining the maximum distance between adjacent terms?

Ed Jeffery

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