[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:
1,2,4,5,6,8,9,10,11,13,14,15,17,...
(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.
Thanks,
Leroy Quet
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