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
Keywords
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
Programs
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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]]]]
Comments