A333993 Square spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the integers forming a square of size k X k, for all k = 1, 2, 3, ..., add up to a number that does not contain the digit 1.

0, 2, 3, 4, 5, 20, 6, 7, 23, 8, 9, 22, 24, 25, 200, 26, 27, 28, 29, 203, 30, 33, 32, 202, 2000, 34, 35, 36, 205, 37, 38, 204, 39, 42, 2002, 40, 43, 90, 59, 84, 46, 2023, 44, 206, 53, 82, 48, 220, 284, 45, 57, 74, 207, 47, 85, 2244, 49, 52, 50, 76, 2043, 273, 20007, 436, 54, 55, 56, 58, 62, 60, 96

Offset

1,2

Comments

This is the lexicographically earliest sequence of distinct nonnegative terms with this property. Computed in memory of Michaël Falcoz, August 2, 1986 - August 20, 2020.

Links

Table of n, a(n) for n=1..71.

Example

No integer in the spiral contains "1"; the integers forming any 2 X 2 square add up to a number without "1"; the integers forming any 3 X 3 square add up to a number without "1", etc.
The 5 X 5 square visible here (without the leg 34-35) is made of 25 terms summing up to 2968, a result that doesn't use the digit 1.
.
     30--33--32-202-2000-34
      |                   |
    203   6---7--23---8  35
      |   |           |   .
     29  20   0---2   9   .
      |   |       |   |   .
     28   5---4---3  22
      |               |
     27--26--200-25--24
.

Crossrefs

Cf. A337115.

Sequence in context: A295317 A165646 A261639 * A362064 A342617 A329579

Adjacent sequences: A333990 A333991 A333992 * A333994 A333995 A333996

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Sep 04 2020

Status

approved