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.
%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