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A163776
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a(n) is the n-th dS-prime (dual Shuffle prime) For N>=2, the family of dual shuffle permutations is defined by p(m,N) = -2m (mod N+1) if N is even, p(m,N) = -2m (mod N) if N is odd and 1<=m<N, p(N,N) = N if N is odd. N is dS-prime if p(m,N) consists of a single cycle of length N. So all dS-primes are even.
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3
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4, 6, 12, 22, 28, 36, 46, 52, 60, 70, 78, 100, 102, 148, 166, 172, 180, 190, 196, 198, 238, 262, 268, 270, 292, 310, 316, 348, 358, 366, 372, 382
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OFFSET
| 1,1
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COMMENTS
| No formula is known for a(n): the dS-primes have been found by exhaustive search. But we have: N is dS-prime iff p=N+1 is an odd prime number and -2 generates Z_p^* (the multiplicative group of Z_p).
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LINKS
| P. R. J. Asveld,Table of n, a(n) for n=1..3612
P. R. J. Asveld, Permuting operations on strings and their relation to prime numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.
P. R. J. Asveld, Permuting operations on strings and the distribution of their prime numbers (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
P. R. J. Asveld, Some Families of Permutations and Their Primes (2009), TR-CTIT-09-27, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
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FORMULA
| Unknown
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EXAMPLE
| For N=6 and N=10 we obtain the permutations (1 5 4 6 2 3) and (1 9 4 3 5)(2 7 8 6 10): 6 is dS-prime, but 10 is not.
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CROSSREFS
| a(n)/2 results in the dual Josephus_2-primes (A163781). Considered as sets a(n)/2 is the union of A163777 and A163780. If b(n) denotes the shuffle primes (A071642), then the union of a(n)/2 and b(n)/2 is equal to the Twist-primes or Queneau numbers (A054639), their intersection is equal to the Archimedes_0-primes (A163777).
Sequence in context: A027150 A020141 A049478 * A050558 A098145 A054167
Adjacent sequences: A163773 A163774 A163775 * A163777 A163778 A163779
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KEYWORD
| nonn
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AUTHOR
| P. R. J. Asveld (infprja(AT)cs.utwente.nl), Aug 13 2009
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