

A240067


Twice prime octonion integers shown as 8vectors sorted by norm and then real and 7 imaginary components.


1



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, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 0, 2, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 2, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0
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OFFSET

1,1


COMMENTS

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 9328 octonions having norm 2. The first 11 are shown above. Counting octonions having just nonnegative entries, there are 309 having norm 2; see A240066.


REFERENCES

John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC, 2003.


LINKS

John C. Baez, The Octonions, arXiv:math/0105155 [math.RA], 20012002.


MATHEMATICA

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, 2, 2}, {b, 2, 2}, {c, 2, 2}, {d, 2, 2}, {e, 2, 2}, {f, 2, 2}, {g, 2, 2}, {h, 2, 2}], 7]]]]


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



