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

0,4

Links

Table of n, a(n) for n=0..84.

Formula

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

Example

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.

Sequence in context: A303040 A302877 A303525 * A133948 A078935 A276774

Adjacent sequences: A368640 A368641 A368642 * A368644 A368645 A368646

Keyword

nonn,easy

Author

Tamas Sandor Nagy, Jan 01 2024

Status

approved