A354435 Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3 X 3 square of numbers sums to a prime, and these primes are distinct.
1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 10, 13, 12, 14, 20, 16, 15, 17, 19, 22, 18, 21, 25, 26, 39, 23, 24, 29, 36, 30, 27, 28, 34, 35, 48, 31, 32, 33, 42, 40, 41, 37, 38, 43, 44, 45, 54, 46, 49, 47, 50, 60, 63, 67, 53, 51, 52, 55, 59, 72, 75, 65, 68, 81, 56, 57, 58, 74, 85, 61, 86, 73, 62, 64, 66, 90, 87
Offset: 1
Examples
The spiral begins
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32--31--48--35--34--28--27 51
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33 15--16--20--14--12 30 53
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42 17 5---4---3 13 36 67
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40 19 6 1---2 10 29 63
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41 22 7---8--11---9 24 60
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37 18--21--25--26--39--23 50
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38--43--44--45--54--46--49--47
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a(9) = 11 as this completes a 3 X 3 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 that has not occurred before.
a(25) = 39 as this completes a 3 X 3 square of numbers 1,2,10,8,11,9,25,26,39 which sum to 131, a prime, and 39 is the smallest unused number to form a prime sum that has not occurred before. Note that 35 would generate a square sum of 127, also a prime, but 127 was formed previously by the 3 X 3 square 19,6,1,22,7,8,18,21,25 so cannot be used. This is the first term to differ from A354441.
Links
- Scott R. Shannon, Image of the first 200000 terms. The green line is y = n.
- Scott R. Shannon, Image of the first 1000000 terms.
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