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

1,2

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.

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A029744, A131117.

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

Sequence in context: A209747 A117744 A366481 * A091732 A299439 A109746

Adjacent sequences: A361694 A361695 A361696 * A361698 A361699 A361700

Keyword

nonn

Author

Kishore Rajesh, Mar 20 2023

Status

approved