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A240067 Twice prime octonion integers shown as 8-vectors 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 (list; graph; refs; listen; history; text; internal format)
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], 2001-2002.
Wikipedia, Octonion
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
Cf. A239395 (twice prime nonnegative Hurwitz quaternions), A240066.
Sequence in context: A180215 A228552 A240066 * A300717 A191928 A359887
KEYWORD
sign
AUTHOR
T. D. Noe, Mar 31 2014
STATUS
approved

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Last modified April 18 03:01 EDT 2024. Contains 371767 sequences. (Running on oeis4.)