Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #28 Aug 05 2024 14:14:17
%S 2,38,57,145,189,2293,2898,6222,7486,26793,45350,90822,177773
%N a(n) is the n-th J_12-prime (Josephus_12 prime).
%C Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 12th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_12-prime if this permutation consists of a single cycle of length N.
%C There are 13 J_12-primes in the interval 2..1000000 only. No formula is known; the J_12-primes were 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 2 is a J_12-prime (trivial).
%Y Cf. A163782 through A163791 for J_2- through J_11-primes.
%Y Cf. A163793 through A163800 for J_13- through J_20-primes.
%K nonn,more
%O 1,1
%A _Peter R. J. Asveld_, Aug 04 2009