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A225215
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Floor of the Euclidean distance of a point on the (1, 1, 1; 1, 1, 1) 3D walk.
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2
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1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 41, 41, 42, 42, 43, 43, 44, 45, 45, 46, 46, 47, 47, 48, 49, 49, 50, 50
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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COMMENTS
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Consider a standard 3-dimensional Euclidean lattice. We take 1 step along the positive x-axis, 1 along the positive y-axis, 1 along the positive z-axis, 1 along the positive x-axis, and so on. After 3, 6, 9, 12, 15 etc steps we have returned to the space diagonal (with equal x, y and z coordinates).
This sequence gives the floor of the Euclidean distance to the origin after n steps.
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LINKS
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FORMULA
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PROG
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(JavaScript)
p = new Array(0, 0, 0);
for (a = 1; a < 100; a++) {
p[a%3] += 1;
document.write(Math.floor(Math.sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2])) + ", ");
}
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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