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A308629
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Lengths between nodes on a square spiral, such that the n-th node is closer to the (n-2)-th node than to the (n-1)-th node.
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1
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1, 2, 4, 4, 5, 6, 8, 6, 10, 10, 9, 12, 13, 11, 15, 15, 15, 17, 18, 17, 20, 21, 19, 23, 24, 22, 26, 26, 24, 29, 29, 27, 32, 31, 30, 35, 33, 32, 38, 36, 35, 41, 38, 38, 44, 41, 39, 48, 43, 42, 51, 45, 45, 53, 48, 47, 56, 51, 50, 59, 53, 52, 62, 56, 55, 65, 58
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OFFSET
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1,2
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COMMENTS
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Consider a square spiral which begins at the origin and spirals counterclockwise. We define (0, 0) and (1, 0) as the first two nodes. From here, we wish to find the first point along the spiral path which is closer to (0, 0) than to (1, 0). This point would be (0, 1), which is 2 unit lengths away from the previous node. Hence 2 is the first number in our sequence. Likewise, 4 is the next number, as we have to travel 4 unit lengths along the square spiral to reach a point closer to (1, 0) than to (0, 1), and so on.
Based on an empirical observation of the first several terms, I conjecture that lim_{n->infinity} a(n)/n = 8/9.
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LINKS
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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