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 A375001 #4 Jul 28 2024 17:02:06
%S A375001 1,2,1,1,2,1,3,1,2,1,1,3,1,2,1,2,2,3,1,2,1,1,2,2,3,1,2,1,4,1,2,2,3,1,
%T A375001 2,1,1,4,1,2,2,3,1,2,1,2,1,4,1,2,2,3,1,2,1,1,1,2,4,1,2,2,3,1,2,1,3,1,
%U A375001 1,2,4,1,2,2,3,1,2,1,1,3,1,1,2,4,1,2,2,3,1,2,1
%N A375001 Square array read by antidiagonals: T(n,k) is the position of the last requested element when the elements of the k-th composition (in standard order) are requested from a self-organizing list initialized to (1, 2, 3, ...), using the move-ahead(n) updating strategy; n >= 0, k >= 1.
%C A375001 See A374996 for details.
%F A375001 T(0,k) = A007814(k) + 1.
%F A375001 T(1,k) = A374998(k).
%F A375001 T(n,k) = A374997(k) if n >= A333766(k)-1.
%F A375001 T(n,k) = A374996(n,k) - A374996(n,A025480(k-1)).
%F A375001 Sum_{j=1..m} T(n,k*2^j+2^(j-1)) = m*(m+1)/2 if m >= A333766(k). This is a consequence of the fact that the first m positions of the list are occupied by the elements 1, ..., m, as long as no element larger than m has been requested so far.
%e A375001 Array begins:
%e A375001 n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e A375001 ---+--------------------------------------------
%e A375001 0 | 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
%e A375001 1 | 1 2 1 3 2 2 1 4 1 1 1 3 2 2 1
%e A375001 2 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 3 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 4 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 5 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 6 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 7 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 8 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 9 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 10 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 11 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 12 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 13 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 14 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%e A375001 15 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
%Y A375001 Cf. A007814, A025480, A374998 (row n=1), A333766, A374996, A374997.
%K A375001 nonn,tabl
%O A375001 0,2
%A A375001 _Pontus von Brömssen_, Jul 27 2024