cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A341216 Triangle read by columns T(n,k) k > n >= 1: Last survivor positions in a modified Josephus problem for n numbers, where after each deletion the counting starts over at the lowest existing number n, rather than continuing from the current position.

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%I A341216 #18 Feb 27 2021 22:13:10
%S A341216 1,1,2,1,1,2,1,2,3,4,1,1,1,1,2,1,2,3,4,5,6,1,1,1,1,1,1,2,1,2,2,3,3,4,
%T A341216 5,6,1,1,2,3,3,3,4,5,6,1,2,3,4,5,6,7,8,9,10,1,1,1,1,1,1,1,1,1,1,2,1,2,
%U A341216 3,4,5,6,7,8,9,10,11,12,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2
%N A341216 Triangle read by columns T(n,k) k > n >= 1: Last survivor positions in a modified Josephus problem for n numbers, where after each deletion the counting starts over at the lowest existing number n, rather than continuing from the current position.
%C A341216 Arrange 1,2,3,...,n clockwise in a circle. Start the count at the lowest surviving value and delete the k-th value counting clockwise around the circle. Repeat this procedure until one number remains, which is T(n,k).
%C A341216 Note: In the complete n X k array with n >= 1 and k >= 1, T(n,k) = T(k-1,k) for all n >= k > 1 and T(n,1)=n.
%C A341216 That makes the bottom triangle of the array unchanging, so it is omitted.
%H A341216 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A341216 T(1,k) = 1, for k > 1;
%F A341216 T(n,k) = T(n-1,k) if k mod n > T(n-1,k) or k mod n = 0;
%F A341216 T(n,k) = T(n-1,k) + 1 otherwise.
%e A341216 n\k    2    3    4    5    6    7    8    9   10   11   12   13
%e A341216 _______________________________________________________________
%e A341216 1      1    1    1    1    1    1    1    1    1    1    1    1
%e A341216 2           2    1    2    1    2    1    2    1    2    1    2
%e A341216 3                2    3    1    3    1    2    2    3    1    3
%e A341216 5                     4    1    4    1    3    3    4    1    4
%e A341216 6                          2    5    1    3    3    5    1    5
%e A341216 7                               6    1    4    3    6    1    6
%e A341216 8                                    2    5    4    7    1    7
%e A341216 9                                         6    5    8    1    8
%e A341216 10                                             6    9    1    9
%e A341216 11                                                 10    1   10
%e A341216 12                                                       2   11
%e A341216 13                                                           12
%Y A341216 The last entry in each column is A128982.
%K A341216 nonn,tabl
%O A341216 1,3
%A A341216 _Gary Yane_, Feb 06 2021