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A163783 a(n) is the n-th J_3-prime (Josephus_3 prime).

%I A163783 #26 Aug 05 2024 14:09:40
%S A163783 3,5,27,89,1139,1219,1921,2155,5775,9047,12437,78785,105909,197559,
%T A163783 1062657
%N A163783 a(n) is the n-th J_3-prime (Josephus_3 prime).
%C A163783 Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 3rd unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_3-prime if this permutation consists of a single cycle of length N.
%C A163783 There are 14 J_3-primes in the interval 2..1000000 only. No formula is known; the J_3-primes have been found by exhaustive search.
%C A163783 a(16) > 3*10^6. - _Bert Dobbelaere_, Apr 20 2019
%D A163783 R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.
%H A163783 P. R. J. Asveld, <a href="http://eprints.eemcs.utwente.nl/20685/">Permuting operations on strings and the distribution of their prime numbers</a> (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
%H A163783 P. R. J. Asveld, <a href="https://citeseerx.ist.psu.edu/pdf/9d8542763057ef03a22b57f87085d69497ddaf46">Permuting Operations on Strings-Their Permutations and Their Primes</a>, Twente University of Technology.
%H A163783 P. R. J. Asveld, <a href="http://dx.doi.org/10.1016/j.dam.2011.07.019">Permuting Operations on Strings and Their Relation to Prime Numbers</a> Discrete Applied Mathematics 159 (2011) 1915-1932.
%H A163783 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%e A163783 All J_3-primes are odd.
%Y A163783 A163782 for J_2-primes. A163784 through A163800 for J_4- through J_20-primes.
%K A163783 nonn,more
%O A163783 1,1
%A A163783 _Peter R. J. Asveld_, Aug 05 2009
%E A163783 a(15) from _Bert Dobbelaere_, Apr 20 2019