Spoiler: Another kind of sequence puzzle
- From: Leroy Quet <qqquet@xxxxxxxxxxxxxx>
- Date: Thu, 02 Aug 2007 11:16:41 -0700
I will post the solution now, even though only a very short while has
passed since I posted the question.
Original message as spoiler-space.
I suspect this 'puzzle' is easy, and I'll probably regret I posted this.
---
Let {c(k)} be as defined at sequence A022940 of the Encyclopedia of
Integer Sequences.
http://www.research.att.com/~njas/sequences/A022940
({c(k)} itself is not in the EIS. I assume that by "compliment" of
sequence A022940, Clark Kimberling means the sequence of those positive
integers which do NOT occur in sequence A022940.)
Define sequence {a(k)} as follows:
Let b(n) = c(n) - n + 1.
a(1) = the number of 1's in {b(k)}. a(2) = the number of 2's in {b(k)}.
In general, a(n) = the number of n's in {b(k)}.
So, {a(k)} begins: 0,1,1,3,5,6,7,9,...
Define {a(k)}. (Define it in a simpler way than by the steps given above.)
Thanks,
Leroy Quet
I get that a(1)=0, a(2)=1. a(n) = c(n-2) -1, for n >= 3.
I don't know if there is a "closed form" (nonrecursive representation)
for {c(k)}.
Thanks,
Leroy Quet
.
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