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A239394
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Number of prime nonnegative Lipschitz quaternions having norm prime(n).
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3
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6, 4, 12, 4, 12, 16, 24, 16, 12, 36, 16, 28, 48, 28, 24, 48, 48, 52, 40, 36, 52, 40, 60, 84, 64, 96, 52, 72, 76, 84, 64, 96, 96, 88, 120, 76, 100, 88, 84, 132, 120, 124, 96, 112, 132, 100, 124, 112, 144, 148, 156, 120, 160, 168, 180, 132, 204, 136, 160, 204
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OFFSET
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1,1
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COMMENTS
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For n > 1, there are prime(n) + 1 more nonnegative Hurwitz quaternions than nonnegative Lipschitz quaternions. - T. D. Noe, Mar 31 2014
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LINKS
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Table of n, a(n) for n=1..60.
Wikipedia, Hurwitz quaternion
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EXAMPLE
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The six prime nonnegative Lipschitz quaternions having norm 2 are 1+i, 1+j, 1+k, i+j, i+k, and j+k.
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MATHEMATICA
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(* first << Quaternions` *) mx = 17; 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] &]; q2 = Sort[q, Norm[#1] < Norm[#2] &]; Transpose[Tally[(Norm /@ q2)^2]][[2]]
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CROSSREFS
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Cf. A239393 (prime Lipschitz quaternions).
Cf. A239395 (prime Hurwitz quaternions).
Sequence in context: A357128 A141270 A040032 * A006582 A263586 A180497
Adjacent sequences: A239391 A239392 A239393 * A239395 A239396 A239397
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Mar 21 2014
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STATUS
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approved
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