A355314 Lexicographically earliest sequence of positive integers on a square spiral such that the difference between all orthogonally adjacent pairs of numbers is distinct.
0, 0, 1, 3, 7, 12, 1, 7, 15, 1, 10, 23, 0, 17, 35, 54, 0, 27, 48, 72, 0, 26, 55, 83, 31, 0, 34, 69, 106, 39, 1, 41, 83, 126, 1, 45, 91, 140, 77, 128, 2, 57, 1, 61, 119, 183, 1, 93, 158, 1, 74, 143, 218, 0, 115, 192, 0, 79, 160, 244, 2, 87, 174, 1, 89, 185, 1, 166, 6, 101, 198, 296, 0, 101, 203, 1
Offset: 0
Keywords
Examples
The spiral begins:
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91--45---1--126-83--41---1 :
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140 0--54--35--17---0 39 115
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77 27 7---3---1 23 106 0
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128 48 12 0---0 10 69 218
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2 72 1---7--15---1 34 143
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57 0--26--55--83--31---0 74
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1--61--119-183--1--93--158--1
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a(8) = 15 as when a(8) is placed, at coordinate (1,-1) relative to the starting square, its two orthogonally adjacent squares are a(1) = 0 and a(7) = 7. The ten previously occurring differences between all orthogonally adjacent pairs up to a(7) are 0, 1, 2, 3, 4, 5, 6, 7, 11, 12. The lowest unused difference is 8 thus a(8) = 15 can be chosen as it results in differences with its two orthogonal neighbors of 15 - 7 = 8 and 15 = 0 = 15, neither of which has previously occurred.
Links
- Scott R. Shannon, Image of the first 500000 terms. The values are scaled across the spectrum from red to violet, with the value ranges increasing towards the violet end to give more color weighting to the larger numbers.
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