[seqfan] Avoiding Backwards Sums

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Mon Jun 1 01:26:31 CEST 2009

Consider the sequence defined as:

a(1) = 1.
For n >=2,
a(n) = the smallest integer > a(n-1) such that
sum{k=1 to r} a(k)
doesn't equal any value of
sum{k=1 to q} a(n+1-k),
for all positive integers n, any positive integer r, and any positive integers q <= n-1.

(The second sum obviously does equal the first sum for q = n = r.)

I get that the sequence {a(k)} starts:
(Unless I made an error.)

Hmmm. Looks like a Beatty sequence, perhaps?

My question is:
Is {a(k)} the same as sequence A141204? (Attn: Paul Hannah.)

This seems like it should be absolutely trivial to prove, if it is, but I don't know where to begin.

Leroy Quet


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