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A055670
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a(n) = (nth prime) - (-1)^(nth prime).
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7
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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, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of right-inequivalent prime Hurwitz quaternions of norm p, where p = n-th rational prime (indexed by A000040).
Two primes are considered right-equivalent if they differ by right multiplication by one of the 24 units. - njas
Start of nth run of consecutive nonprime numbers. Since 2 is the only even prime, for all other prime numbers the expression "- (-1)^(nth prime)" works out to "+ 1." - Alonso del Arte, Oct 18 2011
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REFERENCES
| L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.
Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology, Dover, New York, 1978, page 134
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FORMULA
| a(n) = p(n)+1 = A008864(n) for n >= 2. a(n) = A055669(n)/24.
a(n) = prime(n) + (-1)^(prime(n) + 1) - Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 07 2006
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EXAMPLE
| a(1)=2-(-1)^2=1, a(2)=3-(-1)^3=4.
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MATHEMATICA
| f[n_] = Prime[n] + (-1)^(Prime[n] + 1); Table[f[n], {n, 1, 200}] (* Roger Bagula, Oct 07 2006 *)
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CROSSREFS
| Cf. A000040, A006093.
Cf. A055669-A055672.
a(n) = A083503(p) for n>1.
Sequence in context: A053579 A074121 A175088 * A141096 A089257 A113451
Adjacent sequences: A055667 A055668 A055669 * A055671 A055672 A055673
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), May 02 2001
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.
Edited by N. J. A. Sloane, Aug 16 2009
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