login

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”).

A360268
A version of the Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,...,n in a circle, increasing clockwise. Starting with i=1, delete the integer 5 places clockwise from i. Repeat, counting 5 places from the next undeleted integer, until only one integer remains.
1
1, 1, 1, 3, 4, 4, 3, 1, 7, 3, 9, 3, 9, 1, 7, 13, 2, 8, 14, 20, 5, 11, 17, 23, 4, 10, 16, 22, 28, 4, 10, 16, 22, 28, 34, 4, 10, 16, 22, 28, 34, 40, 3, 9, 15, 21, 27, 33, 39, 45, 51, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 1, 7, 13, 19, 25
OFFSET
1,4
FORMULA
a(n) = (a(n-1) + 5) mod n + 1 if n > 1, a(1) = 1.
EXAMPLE
a(7) = 3 because the elimination process gives (^1,2,3,4,5,6,7) -> (1,2,3,4,5,^7) -> (1,2,3,4,^7) -> (^1,2,3,4) -> (1,^3,4) -> (^3,4) -> (3), where ^ denotes the counting reference position.
a(13) = 9 => a(14) = (a(13) + 5) mod 14 + 1 = 1.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = Mod[a[n - 1] + 5, n] + 1; Array[a, 100] (* Amiram Eldar, Feb 03 2023 *)
PROG
(Python)
def A360268_up_to_n(n):
val = 1
return [val := (val + 5) % i + 1 for i in range(1, n+1)]
CROSSREFS
6th column of A198789.
Sequence in context: A073498 A105736 A248158 * A090283 A318705 A334492
KEYWORD
nonn
AUTHOR
Benjamin Lilley, Jan 31 2023
STATUS
approved