A240066 Twice prime nonnegative 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, 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

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 A374248 A300717

Adjacent sequences: A240063 A240064 A240065 * A240067 A240068 A240069

Keyword

nonn

Author

T. D. Noe, Mar 31 2014

Status

approved