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A239395
Twice prime nonnegative Hurwitz quaternions shown as 4-vectors sorted by norm and then (1,i,j,k) components.
6
2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 3, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 0, 2, 2, 2, 4, 2, 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 3, 3, 1, 1, 3, 1, 3, 1, 3, 1, 1, 3, 2, 4, 0, 0, 2, 0, 4, 0
OFFSET
1,1
COMMENTS
The vectors are multiplied by 2 because a Hurwitz quaternion can have half-integer integer components. The norms of quaternions are (rational) primes 2, 3, 5, 7, 11, ... A quaternion is commonly written a + b*i + c*j + d*k, where 1, i, j, and k are units.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..2612 (4-vectors)
Wikipedia, Hurwitz quaternion.
MATHEMATICA
(* first << Quaternions` *) mx = 5; lst = Flatten[Table[{a, b, c, d}/2, {a, 0, mx}, {b, 0, mx}, {c, 0, mx}, {d, 0, mx}], 3]; q = Select[lst, Norm[Quaternion @@ #] < mx^2 && PrimeQ[Quaternion @@ #, Quaternions -> True] &]; 2*Sort[q, Norm[#1] < Norm[#2] &]
CROSSREFS
Cf. A239393 (Lipschitz quaternions).
Cf. A239396 (number of Hurwitz quaternions having norm prime(n)).
Sequence in context: A062070 A347088 A343991 * A182004 A179851 A347534
KEYWORD
nonn,nice,tabf
AUTHOR
T. D. Noe, Mar 21 2014
STATUS
approved