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).

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

Offset: 1

Author

Kishore Rajesh, Mar 20 2023

Keywords

• nonn

Comments

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.

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

Examples

			The following shows the positioning of the first 5 boxes:
            __ __ __ __
           |   __ __ __|__ __
         __|__|__      |     |
        |  |  |  |     |     |
      __|__|__|__|__ __|     |
     |  |__|__|__|           |
   __|__ __|  |__ __ __ __ __|
  |__|
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program
• Kishore Rajesh, Illustration of first 10 terms of the sequence.

Crossrefs

Cf. A029744, A131117.

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

Programs

PARI

See Links section.