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A354453
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Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 2 X 2 square of numbers sums to a prime, and that prime is unique for all such squares. Start with a(1) = 0.
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4
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0, 1, 2, 4, 3, 6, 5, 8, 14, 7, 9, 17, 10, 12, 19, 21, 11, 18, 16, 32, 13, 23, 25, 20, 30, 15, 27, 40, 31, 43, 22, 28, 39, 37, 36, 41, 24, 51, 57, 48, 35, 69, 26, 49, 66, 53, 65, 58, 76, 29, 61, 88, 38, 90, 33, 113, 34, 54, 123, 67, 86, 74, 100, 98, 42, 75, 91, 70, 96, 102, 71, 117, 44, 106, 126
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OFFSET
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1,3
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COMMENTS
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This is a variation of A337116 where the same rules apply except that the primes generated by all 2 X 2 square sums must be unique. This leads to the terms having a far greater variation in value while being concentrated along a central line which shows wave-like variations in density. See the linked image. The reason for this behavior is unknown.
See A354460 for the successive prime sums formed by each completed 2 X 2 square of numbers.
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LINKS
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EXAMPLE
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The spiral begins
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24--41--36--37--39--28--22 113
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51 11--21--19--12--10 43 33
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57 18 3---4---2 17 31 90
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48 16 6 0---1 9 40 38
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35 32 5---8--14---7 27 88
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69 13--23--25--20--30--15 61
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26--49--66--53--65--58--76--29
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a(9) = 14 as this completes a 2 X 2 square of numbers 0,1,8,14 which sum to 23, a prime, and 14 is the smallest unused number to form a prime sum that has not occurred before. Note that 10 is unused and would form a prime sum of 19, see A337116, but 19 was formed previously by the square 6,0,5,8, so cannot be used. This is the first term to differ from A337116.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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