A350281 Square array filled and read by antidiagonals upwards; the first value is 0; if the previous value has already appeared in the table, then the next value is the square of the distance to the nearest earlier position with the same value; otherwise the next value is 0.

0, 0, 1, 0, 1, 1, 1, 5, 0, 4, 0, 4, 13, 0, 1, 4, 5, 4, 1, 5, 10, 0, 4, 1, 5, 5, 1, 2, 0, 1, 5, 2, 25, 0, 5, 4, 16, 0, 1, 1, 2, 1, 4, 5, 1, 10, 106, 0, 1, 1, 1, 1, 1, 2, 5, 5, 29, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 1, 13, 49, 0, 4, 17, 0, 8, 0, 8, 8, 2, 73, 0, 4, 13, 5, 13, 8, 5, 10, 25, 37, 0

Offset

0,8

Comments

This sequence is a two-dimensional variant of Van Eck's sequence (A181391).

When working on a square spiral, we quickly end with all 1's:

1--1--1--1--1--1--1

| |

1 1--1--0-13--2 1

. | | |

. 1 1--0--1 0 1

. | | | | |

1 4 0--0 5 1

| | | |

1 0--2--0--1 1

| |

1--1--1--1--1--1

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10010

Rémy Sigrist, C++ program

Example

Square array begins:
  n\k|   0    1   2   3   4   5   6  7   8   9
  ---+----------------------------------------
    0|   0    1   1   4   1  10   2  4   1   5
    1|   0    1   0   0   5   1   5  5   2   1
    2|   0    5  13   1   5   0   4  1   1   0
    3|   1    4   4   5  25   1   1  1   8  10
    4|   0    5   1   2   2   1   1  0   5   1
    5|   4    4   5   1   1   1  17  8   5   1
    6|   0    1   1   1   1   4  13  1   1  29
    7|   0    0   0   1   0   5   5  1  25   2
    8|  16  106   0  49  13   1   1  2   5  20
    9|  10   29  13   4   4   1   8  5   0   2

Prog

(C++) See Links section.

Crossrefs

Cf. A001481, A181391.

Sequence in context: A258754 A175296 A076266 * A354053 A200102 A016581

Adjacent sequences: A350278 A350279 A350280 * A350282 A350283 A350284

Keyword

nonn,tabl

Author

Rémy Sigrist, Mar 27 2022

Status

approved