Re: Is there more symmetry to this function?
From: Jaap (jaapsch_at_hotmail.com)
Date: 07/08/04
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Date: 8 Jul 2004 03:19:27 -0700
crowdog@o2online.de (Dement) wrote ...
> Consider the following function:
> f: N x N -> N (N naturals)
> f(1,1) = 16, f(1,2) = 17, f(1,3) = 20, f(1,4) = 25, f(1,5) = 32, ...
> f(2,1) = 33, f(2,2) = 36, f(2,3) = 41, f(2,4) = 48, f(2,5) = 57, ...
> f(3,1) = 52, f(3,2) = 57, f(3,3) = 64, f(3,4) = 73, f(3,5) = 84, ...
> f(4,1) = 73, f(4,2) = 80, f(4,4) = 100, ... etc.
> A similar function: g: Z x Z -> Z
> g(1,1) = 0, g(1,2) = -7, g(1,3) = -12, g(1,4) = -15, ...
> g(2,1) = 9, g(2,2) = 4, g(2,3) = 1, g(2,4) = 0, ...
> g(3,1) = 20, g(3,2) = 17, g(3,3) = 16, ...
> g(4,1) = 33, ...
> My questions:
> Can these functions be stated explicitely (in a simple fashion)?
f(m,n) = 16(m+1) + (n+m-2)^2
g(m,n) = 16(m-2) + (n+m-5)^2
Jaap
-- Jaap's Puzzle Page: http://www.geocities.com/jaapsch/puzzles/
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