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a(n) is the n-th J_5-prime (Josephus_5 prime).
2

%I #22 Aug 05 2024 14:10:44

%S 3,15,17,45,73,83,165,177,181,229,377,383,787,2585,3127,3635,4777,

%T 36417,63337,166705,418411

%N a(n) is the n-th J_5-prime (Josephus_5 prime).

%C Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 5th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_5-prime if this permutation consists of a single cycle of length N.

%C There are 21 J_5-primes in the interval 2..1000000 only. No formula is known; the J_5-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="https://citeseerx.ist.psu.edu/pdf/9d8542763057ef03a22b57f87085d69497ddaf46">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_5-primes are odd.

%Y Cf. A163782 through A163784 for J_2- through J_4-primes.

%Y Cf. A163786 through A163800 for J_6- through J_20-primes.

%K nonn,more

%O 1,1

%A _Peter R. J. Asveld_, Aug 05 2009