A163784 -id:A163784 - cp's OEIS frontend

A163783 a(n) is the n-th J_3-prime (Josephus_3 prime).

3, 5, 27, 89, 1139, 1219, 1921, 2155, 5775, 9047, 12437, 78785, 105909, 197559, 1062657

Offset: 1

Peter R. J. Asveld, Aug 05 2009

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 3rd unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_3-prime if this permutation consists of a single cycle of length N.
There are 14 J_3-primes in the interval 2..1000000 only. No formula is known; the J_3-primes have been found by exhaustive search.
a(16) > 3*10^6. - Bert Dobbelaere, Apr 20 2019

			All J_3-primes are odd.

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

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

A163782 for J_2-primes. A163784 through A163800 for J_4- through J_20-primes.

a(15) from Bert Dobbelaere, Apr 20 2019

A163785 a(n) is the n-th J_5-prime (Josephus_5 prime).

Original entry on oeis.org

3, 15, 17, 45, 73, 83, 165, 177, 181, 229, 377, 383, 787, 2585, 3127, 3635, 4777, 36417, 63337, 166705, 418411

Offset: 1

Peter R. J. Asveld, Aug 05 2009

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.

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.

			All J_5-primes are odd.

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

P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.
P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology, 2014. University link.
Index entries for sequences related to the Josephus Problem

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

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

cp's OEIS Frontend

A163783 a(n) is the n-th J_3-prime (Josephus_3 prime).

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