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A055670
a(n) = prime(n) - (-1)^prime(n).
11
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
OFFSET
1,2
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. - N. J. A. Sloane
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
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.
LINKS
FORMULA
a(n) = prime(n)+1 = A008864(n) for n >= 2. a(n) = A055669(n)/24.
EXAMPLE
a(1) = 2 - (-1)^2 = 1, a(2) = 3 - (-1)^3 = 4.
MATHEMATICA
Join[{1}, Prime[Range[2, 70]]+1] (* Harvey P. Dale, Oct 29 2013 *)
CROSSREFS
a(n) = A083503(p) for n>1.
Sequence in context: A175088 A275671 A370745 * A141096 A089257 A113451
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jun 09 2000
EXTENSIONS
More terms from David W. Wilson, 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, analogs of A055670 and A055672.
Edited by N. J. A. Sloane, Aug 16 2009
STATUS
approved