A361697 - OEIS

%I #28 May 07 2023 06:42:19

%S 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 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 8,53,14,36,1,51,15,35,3,64,7,46,18,56,10,44,9,67

%N 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 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 A029744 appears to be the terms for which a(n)=n in this sequence.

%H Neal Gersh Tolunsky, <a href="/A361697/b361697.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A361697/a361697.gp.txt">PARI program</a>

%H Kishore Rajesh, <a href="/A361697/a361697.png">Illustration of first 10 terms of the sequence</a>.

%e The following shows the positioning of the first 5 boxes:

%e             __ __ __ __

%e            |   __ __ __|__ __

%e          __|__|__      |     |

%e         |  |  |  |     |     |

%e       __|__|__|__|__ __|     |

%e      |  |__|__|__|           |

%e    __|__ __|  |__ __ __ __ __|

%e   |__|

%o (PARI) See Links section.

%Y Cf. A029744, A131117.

%Y Cf. A289523 (analogous sequence with circles), A361742 (variant allowing overlapping edges).

%K nonn

%O 1,2

%A _Kishore Rajesh_, Mar 20 2023