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 A384384 #7 Jun 09 2025 10:38:27 %S A384384 0,1,2,2,3,3,4,3,3,4,4,4,5,5,4,3,4,4,5,4,5,5,6,4,4,5,4,5,5,5,5,4,5,5, %T A384384 5,4,5,5,5,5,5,5,6,6,5,5,6,5,5,5,6,6,6,5,6,5,6,6,6,5,6,6,6,4,5,5,6,5, %U A384384 6,6,6,5,6,6,5,6,6,6,6,5,4,5,5,5,6,6,6,6,6,5,5,6,6,6,7 %N A384384 Length of shortest addition-multiplication-composition chain for n, starting with 1 and x. %C A384384 See A384383 for the definition of addition-multiplication-composition chains. The number n is identified with the constant polynomial p(x) = n. %F A384384 a(n) <= A230697(n). %F A384384 a(n) <= a(n-1) + 1. %e A384384 The smallest n for which a(n) < A230697(n) is n = 31. The length of a shortest addition-multiplication chain for 31 is A230697(31) = 6, but there are addition-multiplication-composition chains of length 5, for example (1, x,) 2*x, 2*x+1, 4*x+3, 7, 31. (4*x+3 is the composition of 2*x+1 with itself; 7 and 31 are the compositions of 4*x+3 with 1 and 7, respectively.) %Y A384384 Cf. A230697 (addition and multiplication), A384383, A384385, A384386, A384483 (addition and composition). %K A384384 nonn %O A384384 1,3 %A A384384 _Pontus von Brömssen_, Jun 01 2025