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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

T. D. Noe, Mar 31 2014

Keywords

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

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]]]]
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