A117282 change request

[N. J. A. Sloane]

shion starting in the positive quadrant. <BR> <BR>The result of this p=
 are: <BR> <BR>(1) What is the sequence of y-values in the positive qu=
 What is the sequence of y-values for non-negative x-values?<BR>The sequenc=
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Date: Tue, 27 May 2008 11:36:21 -0700
From: "Joshua Zucker" <joshua.zucker at gmail.com>
To: "Paul D Hanna" <pauldhanna at juno.com>
Subject: Re: [SeqFans] Beatty Sequences?
Cc: seqfan at ext.jussieu.fr
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Hi Paul and seqfans,
When you do this in the first quadrant only and with the diagonal of
positive slope only, you get beatty sequences related to the golden
ratio.  And those points are also the P-positions for the nim-like
game with two piles where you can take any number from one pile, or an
equal number from both piles simultaneously (the diagonal moves).
http://www.research.att.com/~njas/sequences/A001950 gives one of the
sequences for that problem.

I haven't thought about extending it to all four quadrants so I'm not
sure if I know how to carry out similar proofs here.

But I still suspect it's related to golden ratios, not pi.

I don't know how many terms you generated ... here (below) are the
first quadrant points that my program generated. My program is slow
and stupid so I can't do much bigger than this.   If my program is
right, the sequence of y-values is not in OEIS despite being rather
close to A093609.  The ratio here seems to keep revisiting 1.83333333
... so if it is Beatty then the value ought to be near there
somewhere.  I don't know many special numbers near 11/6.... related to
the golden ratio?  Maybe it's closer to 1.839 or so.

--Joshua Zucker

((1 2)
 (3 5)
 (4 8)
 (6 11)
 (7 13)
 (9 16)
 (10 19)
 (12 22)
 (14 25)
 (15 28)
 (17 31)
 (18 33)
 (20 36)
 (21 39)
 (23 42)
 (24 45)
 (26 48)
 (27 50)
 (29 53)
 (30 56)
 (32 59)
 (34 62)
 (35 65)
 (37 68)
 (38 70)
 (40 73)
 (41 76)
 (43 79)
 (44 81)
 (46 84)
 (47 87)
 (49 90)
 (51 93)
 (52 96)
 (54 99)
 (55 101)
 (57 104)
 (58 107)
 (60 110)
 (61 113)
 (63 116)
 (64 118)
 (66 121)
 (67 124)
 (69 127))