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 A383334 #6 Apr 26 2025 11:27:09 %S A383334 1,2,1,3,2,1,5,3,2,1,7,4,3,2,1,11,6,4,3,2,1,19,8,5,4,3,2,1,29,12,7,5, %T A383334 4,3,2,1,47,20,9,6,5,4,3,2,1,71,29,13,8,6,5,4,3,2,1,127,44,20,10,7,6, %U A383334 5,4,3,2,1,191,70,30,14,9,7,6,5,4,3,2,1 %N A383334 Square array read by antidiagonals: T(n,k) is the smallest positive weight of an n-tuple of nonnegative integers with a shortest vectorial addition chain of length k; n >= 1, k >= 0. %C A383334 See A383333 for details. %C A383334 T(n,k) is the smallest positive degree of a monomial x_1^e_1*...*x_n^e_n that requires k multiplications, given x_1, ..., x_n. %e A383334 Array begins: %e A383334 n\k| 0 1 2 3 4 5 6 7 8 %e A383334 ---+-------------------------- %e A383334 1 | 1 2 3 5 7 11 19 29 47 %e A383334 2 | 1 2 3 4 6 8 12 20 29 %e A383334 3 | 1 2 3 4 5 7 9 13 20 %e A383334 4 | 1 2 3 4 5 6 8 10 14 %e A383334 5 | 1 2 3 4 5 6 7 9 11 %e A383334 The smallest positive weight of a triple of nonnegative integers with a shortest addition chain of length 8 is T(3,8) = 20. Up to permutations, (3,4,13) is the only such triple, with a shortest addition chain [(1,0,0), (0,1,0), (0,0,1),] (0,0,2), (0,0,4), (0,1,4), (1,1,4), (2,2,8), (3,3,12), (3,3,13), (3,4,13). %Y A383334 Cf. A383333. %Y A383334 Rows: A003064 (n=1), A383332 (n=2). %K A383334 nonn,tabl %O A383334 1,2 %A A383334 _Pontus von Brömssen_, Apr 26 2025