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A240066 Twice prime nonnegative octonion integers shown as 8-vectors sorted by norm and then real and 7 imaginary components.

%I A240066 #12 Apr 01 2014 03:23:37
%S A240066 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,
%T A240066 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,
%U A240066 0,1,1,0,2,1,1,0,0,1,0,1,2,1,1,0,0,0,1,1
%N A240066 Twice prime nonnegative octonion integers shown as 8-vectors sorted by norm and then real and 7 imaginary components.
%C A240066 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.
%D A240066 John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC, 2003.
%H A240066 T. D. Noe, <a href="/A240066/b240066.txt">Table of n, a(n) for n = 1..309</a> (8-vectors)
%H A240066 John C. Baez, <a href="http://arxiv.org/abs/math/0105155v4">The Octonions</a>, arxiv.org, 0105155v4, Apr 23 2004
%H A240066 Wikipedia, <a href="http://en.wikipedia.org/wiki/Octonion">Octonion</a>
%e A240066 The first primes listed are 1 + i and 1 + (i+j+k+l)/2.
%t A240066 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]]]]
%Y A240066 Cf. A239395 (twice prime nonnegative Hurwitz quaternions), A240067.
%K A240066 nonn
%O A240066 1,1
%A A240066 _T. D. Noe_, Mar 31 2014