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A361697 The least y-value of the lower left corner of an n X n box with x-value n such that no edge of the box overlaps with a previous box, given that the first box has its lower left corner at (1,1).

%I A361697 #28 May 07 2023 06:42:19
%S A361697 1,2,3,4,2,6,3,8,4,7,9,12,1,11,3,16,2,13,4,17,5,20,6,24,8,14,1,25,7,
%T A361697 21,3,32,10,22,9,31,2,23,11,37,4,26,12,42,13,29,5,48,16,33,6,40,17,28,
%U A361697 8,53,14,36,1,51,15,35,3,64,7,46,18,56,10,44,9,67
%N A361697 The least y-value of the lower left corner of an n X n box with x-value n such that no edge of the box overlaps with a previous box, given that the first box has its lower left corner at (1,1).
%C A361697 The sequence is defined by the following method: Draw a 1 X 1 box with lower left corner at (1,1) on the coordinate grid. Then, for all integers n greater than 1, a(n) is the smallest positive integer value such that an n X n box with lower left coordinate (n, a(n)) has no edges that overlap with other boxes.
%C A361697 A029744 appears to be the terms for which a(n)=n in this sequence.
%H A361697 Neal Gersh Tolunsky, <a href="/A361697/b361697.txt">Table of n, a(n) for n = 1..10000</a>
%H A361697 Rémy Sigrist, <a href="/A361697/a361697.gp.txt">PARI program</a>
%H A361697 Kishore Rajesh, <a href="/A361697/a361697.png">Illustration of first 10 terms of the sequence</a>.
%e A361697 The following shows the positioning of the first 5 boxes:
%e A361697             __ __ __ __
%e A361697            |   __ __ __|__ __
%e A361697          __|__|__      |     |
%e A361697         |  |  |  |     |     |
%e A361697       __|__|__|__|__ __|     |
%e A361697      |  |__|__|__|           |
%e A361697    __|__ __|  |__ __ __ __ __|
%e A361697   |__|
%o A361697 (PARI) See Links section.
%Y A361697 Cf. A029744, A131117.
%Y A361697 Cf. A289523 (analogous sequence with circles), A361742 (variant allowing overlapping edges).
%K A361697 nonn
%O A361697 1,2
%A A361697 _Kishore Rajesh_, Mar 20 2023