A354441 Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3X3 square of numbers sums to a prime.

1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 10, 13, 12, 14, 20, 16, 15, 17, 19, 22, 18, 21, 25, 26, 35, 23, 24, 27, 28, 30, 29, 31, 33, 37, 41, 36, 32, 34, 43, 38, 40, 52, 39, 42, 66, 48, 45, 44, 46, 47, 49, 54, 50, 56, 51, 57, 53, 55, 61, 72, 67, 59, 58, 62, 60, 63, 71, 68, 74, 76, 70, 80, 64, 65, 69, 77, 73

Offset: 1

Author

Scott R. Shannon, May 29 2022

Keywords

• nonn

Comments

See A354442 for the successive prime sums formed by each completed 3X3 square of numbers.

Examples

			The spiral begins
                                .
                                .
   32--36--41--37--33--31--29  57
    |                       |   |
   34  15--16--20--14--12  30  51
    |   |               |   |   |
   43  17   5---4---3  13  28  56
    |   |   |       |   |   |   |
   38  19   6   1---2  10  27  50
    |   |   |           |   |   |
   40  22   7---8--11---9  24  54
    |   |                   |   |
   52  18--21--25--26--35--23  49
    |                           |
   39--42--66--48--45--44--46--47
.
.
a(9) = 11 as this completes a 3X3 square of numbers 5,4,3,6,1,2,7,8,11, which sum to 47, a prime, and 11 is the smallest unused number to form a prime sum.
a(12) = 13 as this completes a 3X3 square of numbers 8,11,9,1,2,10,4,3,13, which sum to 61, a prime, and 13 is the smallest unused number to form a prime sum.
		

Links

• Scott R. Shannon, Image of the first 4000 terms. The green line is y = n.

Crossrefs

Cf. A354442, A337116, A257339, A354434, A000040.