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

1,1

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

Table of n, a(n) for n=1..88.

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 * A374248 A300717 A191928

Adjacent sequences: A240064 A240065 A240066 * A240068 A240069 A240070

Keyword

sign

Author

T. D. Noe, Mar 31 2014

Status

approved