%I #28 Aug 05 2024 14:14:48

%S 5,57,117,187,251,273,275,665,2511,40393,48615,755921,970037

%N a(n) is the n-th J_13-prime (Josephus_13 prime).

%C Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 13th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_13-prime if this permutation consists of a single cycle of length N.

%C There are 13 J_13-primes in the interval 2..1000000 only. No formula is known; the J_13-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_13-primes are odd.

%Y Cf. A163782 through A163792 for J_2- through J_12-primes.

%Y Cf. A163794 through A163800 for J_14- through J_20-primes.

%K nonn,more

%O 1,1

%A _Peter R. J. Asveld_, Aug 04 2009