A163798 -id:A163798 - cp's OEIS frontend

A163797 a(n) is the n-th J_17-prime (Josephus_17 prime).

3, 5, 7, 39, 93, 267, 557, 2389, 2467, 4059, 4681, 6213, 70507, 151013, 282477, 421135, 1272901

Offset: 1

Peter R. J. Asveld, Aug 04 2009

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 17th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_17-prime if this permutation consists of a single cycle of length N.

There are 16 J_17-primes in the interval 2..1000000 only. No formula is known; the J_17-primes have been found by exhaustive search.

			All J_17-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 A163796 for J_2- through J_16-primes.

Cf. A163798 through A163800 for J_18- through J_20-primes.

a(17) from Jinyuan Wang, Jul 05 2025

A163799 a(n) is the n-th J_19-prime (Josephus_19 prime).

Original entry on oeis.org

15, 145, 149, 243, 259, 449, 1921, 2787, 15871, 18563, 26459, 191515, 283269, 741343, 844805

Offset: 1

Peter R. J. Asveld, Aug 04 2009

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 19th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_19-prime if this permutation consists of a single cycle of length N.

There are 15 J_19-primes in the interval 2..1000000 only. No formula is known; the J_19-primes have been found by exhaustive search.

			All J_19-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 A163798 and A163800 for J_2- through J_18- and J_20-primes.

cp's OEIS Frontend

A163797 a(n) is the n-th J_17-prime (Josephus_17 prime).

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