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%I #27 Sep 16 2022 09:41:15
%S 15,145,149,243,259,449,1921,2787,15871,18563,26459,191515,283269,
%T 741343,844805
%N a(n) is the n-th J_19-prime (Josephus_19 prime).
%C Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 19th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_19-prime if this permutation consists of a single cycle of length N.
%C There are 15 J_19-primes in the interval 2..1000000 only. No formula is known; the J_19-primes have been found by exhaustive search.
%D R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.
%H 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 P. R. J. Asveld, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.1682">Permuting Operations on Strings-Their Permutations and Their Primes</a>, Twente University of Technology, 2014. <a href="http://doc.utwente.nl/67513">University link</a>.
%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%e All J_19-primes are odd.
%Y Cf. A163762 through A163798 and A163800 for J_2- through J_18- and J_20-primes.
%K nonn,more
%O 1,1
%A _Peter R. J. Asveld_, Aug 04 2009
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