A337117 Spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the four integers forming any 2 X 2 square add up to a palindrome.

0, 1, 2, 3, 4, 15, 5, 13, 8, 6, 7, 12, 9, 10, 18, 19, 11, 21, 26, 20, 14, 16, 32, 24, 17, 22, 43, 45, 35, 55, 23, 34, 46, 25, 37, 44, 27, 29, 38, 36, 39, 28, 30, 49, 42, 31, 54, 56, 66, 33, 40, 76, 48, 53, 59, 65, 41, 52, 62, 60, 50, 69, 72, 79, 47, 89, 57, 67, 61, 86, 99

Offset

1,3

Comments

This is the lexicographically earliest permutation of the nonnegative integers with this property.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..2757

Example

The four integers inside each of the four 2 X 2 squares that contain 0 sum up to a palindrome: 0+1+2+3=6 / 0+3+4+15=22 / 0+15+5+13=33 / 0+13+8+1=22. This is true for any 2 X 2 square picked up on the (infinite) grid: the upper right corner below sums up to 88 for instance (17+22+43+6).
.
     14--16--32--24--17--22
      |                   |
     20   5--13-- 8---6  43
      |   |           |
     26  15   0---1   7
      |   |       |   |
     21   4---3---2  12
      |               |
     11--19--18--10-- 9
.

Crossrefs

Cf. A214176, A337116 (same idea, with primes instead of palindromes), A337115 (squares instead of palindromes).

Sequence in context: A102483 A134916 A085100 * A204983 A249623 A367742

Adjacent sequences: A337114 A337115 A337116 * A337118 A337119 A337120

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 16 2020

Status

approved