A337116 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 prime.

0, 1, 2, 4, 3, 6, 5, 8, 10, 7, 11, 9, 12, 14, 17, 13, 15, 16, 18, 24, 19, 23, 25, 28, 22, 20, 30, 31, 32, 26, 21, 38, 33, 37, 34, 27, 29, 36, 40, 35, 50, 44, 39, 47, 42, 41, 43, 46, 49, 45, 53, 48, 54, 56, 59, 51, 52, 55, 65, 57, 64, 58, 60, 63, 61, 70, 62, 73, 75, 67

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 16 2020

Keywords

• nonn

Comments

This is (by definition) the lexicographically earliest permutation of the nonnegative integers with this property.

Examples

			The four integers inside each of the four 2 X 2 squares that contain 0 sum up to a prime: 0+1+2+4=7 / 0+4+3+6=13 / 0+6+5+8=19 / 0+8+10+1=19. This is true for any 2 X 2 square picked up on the (infinite) grid: the upper right corner below sums up to the prime 79 for instance (22+20+30+7).
.
     19--23--25--28--22--20
      |                   |
     24   5---8--10---7  30
      |   |           |   .
     18   6   0---1  11   .
      |   |       |   |   .
     16   3---4---2   9   .
      |               |
     15--13--17--14--12
.
		

Links

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

Crossrefs

Cf. A214176, A337115 (same idea, with squares instead of primes), A337117 (with palindromes instead of primes), A337368 (with pandigitals).