A239396 Number of prime nonnegative Hurwitz quaternions having norm prime(n).

6, 8, 18, 12, 24, 30, 42, 36, 36, 66, 48, 66, 90, 72, 72, 102, 108, 114, 108, 108, 126, 120, 144, 174, 162, 198, 156, 180, 186, 198, 192, 228, 234, 228, 270, 228, 258, 252, 252, 306, 300, 306, 288, 306, 330, 300, 336, 336, 372, 378, 390, 360, 402, 420, 438

Offset: 1

Author

T. D. Noe, Mar 21 2014

Keywords

• nonn

Comments

For n > 1, there are prime(n) + 1 more nonnegative Hurwitz quaternions than nonnegative Lipschitz quaternions. - T. D. Noe, Mar 31 2014

Examples

			The six prime nonnegative Hurwitz quaternions having norm 2 are 1+i, 1+j, 1+k, i+j, i+k, and j+k.
		

Links

• Wikipedia, Hurwitz quaternion

Crossrefs

Cf. A239393 (prime Lipschitz quaternions).

Cf. A239395 (prime Hurwitz quaternions).

Programs

Mathematica

(* first << Quaternions` *) mx = 17; 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] &]; q2 = Sort[q, Norm[#1] < Norm[#2] &]; Take[Transpose[Tally[(Norm /@ q2)^2]][[2]], mx]