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A240066
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Twice prime nonnegative octonion integers shown as 8-vectors sorted by norm and then real and 7 imaginary components.
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2
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2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 1
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OFFSET
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1,1
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COMMENTS
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The norm of an octonion is the sum of the squares of its components. Some authors use the square root of that number. There are 309 nonnegative octonions having norm 2. The first 11 are shown above. Counting octonions having both positive and negative entries, there are 9328 having norm 2; see A240067.
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REFERENCES
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John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC, 2003.
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LINKS
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EXAMPLE
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The first primes listed are 1 + i and 1 + (i+j+k+l)/2.
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MATHEMATICA
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Reverse[Rest[Union[Flatten[Table[If[(a/2)^2 + (b/2)^2 + (c/2)^2 + (d/2)^2 + (e/2)^2 + (f/2)^2 + (g/2)^2 + (h/2)^2 == 2, {a, b, c, d, e, f, g, h}, {0}], {a, 0, 2}, {b, 0, 2}, {c, 0, 2}, {d, 0, 2}, {e, 0, 2}, {f, 0, 2}, {g, 0, 2}, {h, 0, 2}], 7]]]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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