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

Author

T. D. Noe, Mar 31 2014

Keywords

• nonn

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.

Examples

			The first primes listed are 1 + i and 1 + (i+j+k+l)/2.
		

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

Crossrefs

Cf. A239395 (twice prime nonnegative Hurwitz quaternions), A240067.

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, 0, 2}, {b, 0, 2}, {c, 0, 2}, {d, 0, 2}, {e, 0, 2}, {f, 0, 2}, {g, 0, 2}, {h, 0, 2}], 7]]]]