A239393 Nonnegative prime Lipschitz quaternions shown as 4-vectors sorted by norm and then (1,i,j,k) components.

1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 0, 0, 1, 0, 2, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 1, 2

Offset

1,41

Comments

A Lipschitz quaternion has all 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..2586 (4-vectors)

Wikipedia , Hurwitz quaternion

Example

The first six nonnegative prime Lipschitz quaternions are 1+i, 1+j, 1+k, i+j, i+k, and j+k.

Mathematica

(* first << Quaternions` *) mx = 5; lst = Flatten[Table[{a, b, c, d}, {a, 0, mx}, {b, 0, mx}, {c, 0, mx}, {d, 0, mx}], 3]; q = Select[lst, Norm[Quaternion @@ #] < mx^2 && PrimeQ[Quaternion @@ #, Quaternions -> True] &]; Sort[q, Norm[#1] < Norm[#2] &]

Crossrefs

Cf. A239394 (number of Lipschitz quaternions having norm prime(n)).

Cf. A239395 (Hurwitz quaternions).

Sequence in context: A176202 A040081 A066745 * A256637 A113063 A123477

Adjacent sequences: A239390 A239391 A239392 * A239394 A239395 A239396

Keyword

nonn,nice

Author

T. D. Noe, Mar 21 2014

Status

approved