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A240066 Twice prime nonnegative octonion integers shown as 8-vectors sorted by norm and then real and 7 imaginary components. 2
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 (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 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.
REFERENCES
John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC, 2003.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..309 (8-vectors)
John C. Baez, The Octonions, arxiv.org, 0105155v4, Apr 23 2004
Wikipedia, Octonion
EXAMPLE
The first primes listed are 1 + i and 1 + (i+j+k+l)/2.
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, 0, 2}, {b, 0, 2}, {c, 0, 2}, {d, 0, 2}, {e, 0, 2}, {f, 0, 2}, {g, 0, 2}, {h, 0, 2}], 7]]]]
CROSSREFS
Cf. A239395 (twice prime nonnegative Hurwitz quaternions), A240067.
Sequence in context: A098939 A180215 A228552 * A240067 A300717 A191928
KEYWORD
nonn
AUTHOR
T. D. Noe, Mar 31 2014
STATUS
approved

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Last modified April 12 16:20 EDT 2024. Contains 371635 sequences. (Running on oeis4.)