A363824 a(0) = 0; for n > 0, a(n) is the total number of other numbers, being constructed on a square spiral, that are visible from a(n-1) that equal a(n-1).

0, 0, 1, 0, 2, 0, 2, 0, 3, 0, 3, 1, 1, 2, 2, 3, 2, 2, 5, 0, 3, 2, 4, 0, 5, 0, 4, 1, 3, 3, 4, 1, 3, 4, 1, 3, 5, 1, 4, 1, 5, 2, 5, 2, 6, 0, 4, 2, 7, 0, 4, 5, 4, 4, 5, 3, 6, 1, 5, 3, 5, 4, 9, 0, 4, 6, 1, 8, 0, 9, 1, 7, 0, 10, 0, 10, 0, 9, 2, 7, 2, 6, 3, 6, 3, 6, 1, 7, 2, 9, 1, 7, 3, 6, 4, 7, 2, 8, 0

Offset: 0

Author

Scott R. Shannon, Oct 19 2023

Keywords

• nonn
• look

Comments

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

Examples

			The spiral begins:
.
                                .
    5---3---1---4---3---1---4   :
    |                       |   :
    1   2---3---2---2---1   3   5
    |   |               |   |   |
    4   2   2---0---1   1   3   4
    |   |   |       |   |   |   |
    1   5   0   0---0   3   1   4
    |   |   |           |   |   |
    5   0   2---0---3---0   4   5
    |   |                   |   |
    2   3---2---4---0---5---0   4
    |                           |
    5---2---6---0---4---2---7---0
.
a(1) = 0 as a(0) = 0, and there are currently no other numbers that equal 0.
a(2) = 1 as a(1) = 0, and from a(1), at (1,0) relative to the starting square, there is currently one other visible 0, namely a(0).
a(6) = 2 as a(5) = 0, and from a(5), at (-1,0) relative to the starting square, there are currently two other visible 0's, namely a(0) and a(3). Note that a(1) = 0 is not visible as it is hidden by a(0).
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..10000
• Scott R. Shannon, Image of the first 500000 terms.
• Scott R. Shannon, Image of the first 10000 terms on the square spiral The colors are graduated across the spectrum to show their relative size. Zoom in to see the numbers.

Crossrefs

Cf. A331400, A357991, A357985, A347358, A347357.