A163784 a(n) is the n-th J_4-prime (Josephus_4 prime).

2, 5, 10, 369, 609, 1841, 2462, 3297, 3837, 14945, 94590, 98121, 965013, 1634157

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 4th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_4-prime if this permutation consists of a single cycle of length N.

There are 13 J_4-primes in the interval 2..1000000 only. No formula is known; the J_4-primes have been found by exhaustive search.

a(15) > 3*10^6. - Bert Dobbelaere, Apr 20 2019

References

R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.

Links

Table of n, a(n) for n=1..14.

P. R. J. Asveld, Permuting operations on strings and the distribution of their prime numbers (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.

P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology.

P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.

Index entries for sequences related to the Josephus Problem

Example

2 is a J_4-prime (trivial).

Crossrefs

A163782 through A163783 for J_2- through J_3-primes. A163785 through A163800 for J_5- through J_20-primes.

Sequence in context: A342489 A342612 A342490 * A215615 A018862 A332009

Adjacent sequences: A163781 A163782 A163783 * A163785 A163786 A163787

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Extensions

a(14) from Bert Dobbelaere, Apr 20 2019

Status

approved