[seqfan] A220952 "unkn" (author Don Knuth, Feb 20, 2013) - continuation?

Richard J. Mathar mathar at mpia-hd.mpg.de
Fri Aug 25 13:23:58 CEST 2017

Referring to http://list.seqfan.eu/pipermail/seqfan/2017-August/017883.html

gf> I think that a(n=0..125) should read:
gf> 1, 2,3,4,9, 14,19,18,17,16,11,12,13,8,7,6,5,10,15,20,21,22,23,24,
gf> 49,74,99,98,97,96,95,90...

The solution is not correct because 96 and 95 are not adjacent.
[96 = 341_5, 95=340_5; the points (3,1) and (3,0) obtained
by pairing the first and last digits are not adjacent in Knuth's meander on 5x5.
(3,0) is horizontally adjacent to (2,0) and (4,0). 
(3,1) is horizontally adjacent to (2,1) and vertically to (3,2)].

My counter-proposal is in http://oeis.org/draft/A220952 .
After 96 =341_5 we have 71=241_5 where (3,4) and (2,4) are horizontally
adjacent, (3,1) and (2,1) are horizontally adjacent, and (4,1), (4,1) are not
to be compared.)

Note that you don't need access to the solutions paper. All we need
to construct the sequence is the assertion that each number (>0)
has exactly two neighbors, and then to find a(n) recursively  by
testing all integers, rejecting a(n-1). This is the "slow" process
implemented in Maple in A220952.


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