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 A240067 Twice prime octonion integers shown as 8-vectors sorted by norm and then real and 7 imaginary components. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A300717 A191928 A359887 Adjacent sequences: A240064 A240065 A240066 * A240068 A240069 A240070 KEYWORD sign AUTHOR T. D. Noe, Mar 31 2014 STATUS approved

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Last modified April 18 03:01 EDT 2024. Contains 371767 sequences. (Running on oeis4.)