login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240068 Number of prime Lipschitz quaternions having norm prime(n). 1
24, 32, 48, 64, 96, 112, 144, 160, 192, 240, 256, 304, 336, 352, 384, 432, 480, 496, 544, 576, 592, 640, 672, 720, 784, 816, 832, 864, 880, 912, 1024, 1056, 1104, 1120, 1200, 1216, 1264, 1312, 1344, 1392, 1440, 1456, 1536, 1552, 1584, 1600, 1696, 1792 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence counts all prime Lipschitz quaternions having a given norm; A239394 counts only the prime nonnegative Lipschitz quaternions.
LINKS
FORMULA
a(n) = 8 * (prime(n) + 1) = 8 * A008864(n).
MATHEMATICA
(* first << Quaternions` *)
mx = 17; lst = Flatten[Table[{a, b, c, d}, {a, -mx, mx}, {b, -mx, mx}, {c, -mx, mx}, {d, -mx, 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]
CROSSREFS
Cf. A239393 (prime Lipschitz quaternions), A239394.
Cf. A055669 (number of prime Hurwitz quaternions of norm prime(n)).
Sequence in context: A102374 A364353 A317534 * A269424 A319928 A025102
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 01 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 03:36 EDT 2024. Contains 371850 sequences. (Running on oeis4.)