A357991 Lexicographically earliest counterclockwise square spiral constructed using the nonnegative integers so that a(n) plus all other numbers currently visible from the current number form a distinct sum; start with a(0) = 0.

0, 1, 1, 1, 2, 1, 3, 0, 4, 0, 0, 0, 1, 5, 0, 6, 0, 0, 1, 0, 2, 4, 0, 7, 0, 8, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 0, 12, 0, 13, 0, 16, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 12, 0, 22, 0, 19, 0, 20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 25, 0, 24, 0, 20, 1, 26, 0, 28, 0, 26, 0, 31, 0, 31, 0, 0, 0, 0

Offset: 0

Author

Scott R. Shannon, Oct 23 2022

Keywords

• nonn

Comments

A number is visible from the current number if, given that it has coordinates (x,y) relative to the current number, the greatest common divisor of |x| and |y| is 1.

In the first 50000 terms the smallest number that has not appeared is 9; it is unknown if all the positive numbers eventually appear.

Examples

			The spiral begins:
.
                       .
                       .
   0---6---0---5---1   7
   |               |   |
   0   2---1---1   0   0
   |   |       |   |   |
   1   1   0---1   0   7
   |   |           |   |
   0   3---0---4---0   0
   |                   |
   2---4---0---7---0---8
.
.
a(6) = 3 as from square 6, at (-1,-1) relative to the starting square, the numbers currently visible are 1 (at -1,0), 0 (at 0,0), 1 (at 1,0), and 1 (at 0,1). These three numbers sum to 3, so a(6) = 3 so that 3 + 3 = 6, the smallest sum that has not previous occurred.
a(8) = 4 as from square 8, at (1,-1) relative to the starting square, the numbers currently visible are 0 (at 0,-1), 1 (at -1,0), 0 (at 0,0), 1 (at 1,0), and 1 (at 0,1). These five numbers sum to 3, so a(8) = 4 so that 3 + 4 = 7, the smallest sum that has not previous occurred. Note that a(7) = 0 and forms a sum of 8.
		

Crossrefs

Cf. A357985, A307834, A275609, A274640, A355270.