A368643 Manhattan distance from the origin of triangular number point T(n) = n*(n+1)/2 in a square spiral with point 0 at the origin.

0, 1, 1, 2, 2, 3, 3, 4, 6, 3, 7, 6, 6, 9, 5, 10, 8, 9, 11, 8, 14, 9, 13, 12, 12, 17, 9, 18, 14, 15, 19, 12, 22, 15, 19, 20, 16, 25, 15, 24, 20, 21, 27, 16, 30, 21, 25, 28, 20, 35, 21, 30, 28, 25, 35, 20, 36, 27, 31, 36, 24, 43, 27, 36, 36, 29, 45, 26, 42, 35, 35, 44, 28, 49, 33, 42, 44, 33, 55, 32, 48, 43, 39, 54, 30

Offset: 0

Author

Tamas Sandor Nagy, Jan 01 2024

Keywords

• nonn
• easy

Examples

			Showing the Manhattan distance for a(4), that is, from the origin to the fourth triangular number T(4) = 10, as being 2:
  +----15-----+-----+-----+     +
  |                       |     |
  |                       |     |
  +     +-----3-----+     +    28
  |     |           |     |     |
  |     |           |     |     |
  +     +     0-----1    10     +
  |     |     ^---a(4)=2--^     |
  |     |                 |     |
  +     6-----+-----+-----+     +
  |                             |
  |                             |
  +----21-----+-----+-----+-----+
		

Crossrefs

Cf. A214526, A000217.

Formula

a(n) = A214526(n*(n+1)/2 + 1).