A331348 Fill an infinite square array by following a spiral around the origin; if the square at position (x, y) is empty then set either T(x, y) = 1 or T(x, y) = T(2*x, 2*y) = 2 such that the RUNS transform of the sequence of values as they are chosen equals the sequence of values as they are visited; first choose the value 1. This sequence corresponds to the values as they are visited.

1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1

Offset

0,2

Comments

The sequence {a(n}} gives the values as they are visited, while, say {b(n)}, gives the values as they are chosen; so:

- a "2" will account for two terms in {a(n)} and for one term in {b(n)},

- a "1" will account for one term in both sequences,

- {a(n)} = RUNS({b(n)}).

Links

Table of n, a(n) for n=0..86.

Rémy Sigrist, PARI program for A331348

Rémy Sigrist, Scatterplot of (x, y) such that T(x, y)=1 and -500 <= x, y, <= 500

Example

The central portion of the spiral is:
      1---2---1---1---2---1---1
      |                       |
      1   2---1---1---2---2   2
      |   |               |   |
      2   1   1---1---2   2   1
      |   |   |       |   |   |
      2   2   2   1---2   2   2
      |   |   |           |   |
      1   1   1---2---2---1   2
      |   |                   |
      1   2---2---2---1---2---1
      |
      2---1---1---2---1---1---2 ...

Prog

(PARI) See Links section.

Crossrefs

See A331349 for the sequence of values as they are chosen.

See A331034 for a similar sequence.

Sequence in context: A078880 A000002 A074295 * A236479 A116514 A334028

Adjacent sequences: A331345 A331346 A331347 * A331349 A331350 A331351

Keyword

nonn,tabl

Author

Rémy Sigrist, Jan 14 2020

Status

approved