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A354441
Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3X3 square of numbers sums to a prime.
8
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
1,2
COMMENTS
See A354442 for the successive prime sums formed by each completed 3X3 square of numbers.
LINKS
Scott R. Shannon, Image of the first 4000 terms. The green line is y = n.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, May 29 2022
STATUS
approved