Search: id:A055670
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%I A055670
%S A055670 1,4,6,8,12,14,18,20,24,30,32,38,42,44,48,54,60,62,68,72,74,80,84,90,98,
%T A055670 102,104,108,110,114,128,132,138,140,150,152,158,164,168,174,180,182,192,
%U A055670 194,198,200,212,224,228,230,234,240,242,252,258,264,270,272,278,282,284
%N A055670 a(n) = (nth prime) - (-1)^(nth prime).
%C A055670 Number of right-inequivalent prime Hurwitz quaternions of norm p, where 
               p = n-th rational prime (indexed by A000040).
%C A055670 Two primes are considered right-equivalent if they differ by right multiplication 
               by one of the 24 units.
%D A055670 L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.
%D A055670 Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology, 
               Dover, New York, 1978, page 134
%F A055670 a(n) = p(n)+1 = A008864(n) for n >= 2. a(n) = A055669(n)/24.
%F A055670 a(n) = Prime[n] + (-1)^(Prime[n] + 1) - Roger Bagula (rlbagulatftn(AT)yahoo.com), 
               Oct 07 2006
%e A055670 a(1)=2-(-1)^2=1, a(2)=3-(-1)^3=4.
%t A055670 f[n_] = Prime[n] + (-1)^(Prime[n] + 1); Table[f[n], {n, 1, 200}] - Roger 
               Bagula (rlbagulatftn(AT)yahoo.com), Oct 07 2006
%Y A055670 Cf. A000040, A006093.
%Y A055670 Cf. A055669-A055672.
%Y A055670 a(n) = A083503(p) for n>1.
%Y A055670 Sequence in context: A028876 A053579 A074121 this_sequence A141096 A089257 
               A113451
%Y A055670 Adjacent sequences: A055667 A055668 A055669 this_sequence A055671 A055672 
               A055673
%K A055670 nonn,easy,nice
%O A055670 1,2
%A A055670 N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
%E A055670 More terms from David W. Wilson (davidwwilson(AT)comcast.net), May 02 
               2001
%E A055670 I would also like to get the sequences of inequivalent prime Hurwitz 
               quaternions, where two primes are considered equivalent if they differ 
               by left or right multiplication by one of the 24 units. This will 
               give two more sequences, analogues of A055670 and A055672.
%E A055670 Edited by N. J. A. Sloane, Aug 16 2009

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