A240067 Twice prime octonion integers shown as 8-vectors sorted by norm and then real and 7 imaginary components.

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

Offset: 1

Author

T. D. Noe, Mar 31 2014

Keywords

• sign

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

Crossrefs

Cf. A239395 (twice prime nonnegative Hurwitz quaternions), A240066.

Programs

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]]]]