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A055670 a(n) = prime(n) - (-1)^prime(n).

%I A055670 #37 Apr 28 2018 07:42:56
%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,
%T A055670 98,102,104,108,110,114,128,132,138,140,150,152,158,164,168,174,180,
%U A055670 182,192,194,198,200,212,224,228,230,234,240,242,252,258,264,270,272,278,282,284
%N A055670 a(n) = prime(n) - (-1)^prime(n).
%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. - _N. J. A. Sloane_
%C A055670 Start of n-th run of consecutive nonprime numbers. Since 2 is the only even prime, for all other prime numbers the expression "- (-1)^(n-th prime)" works out to "+ 1." - _Alonso del Arte_, Oct 18 2011
%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.
%H A055670 Shawn A. Broyles, <a href="/A055670/b055670.txt">Table of n, a(n) for n = 1..20000</a>
%F A055670 a(n) = prime(n)+1 = A008864(n) for n >= 2. a(n) = A055669(n)/24.
%e A055670 a(1) = 2 - (-1)^2 = 1, a(2) = 3 - (-1)^3 = 4.
%t A055670 Join[{1},Prime[Range[2,70]]+1] (* _Harvey P. Dale_, Oct 29 2013 *)
%Y A055670 Cf. A000040, A006093.
%Y A055670 Cf. A055669-A055672.
%Y A055670 a(n) = A083503(p) for n>1.
%K A055670 nonn,easy,nice
%O A055670 1,2
%A A055670 _N. J. A. Sloane_, Jun 09 2000
%E A055670 More terms from _David W. Wilson_, 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, analogs of A055670 and A055672.
%E A055670 Edited by _N. J. A. Sloane_, Aug 16 2009