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 A384383 #7 Jun 09 2025 10:38:35 %S A384383 2,4,14,73,586,7250 %N A384383 Number of polynomials with a shortest addition-multiplication-composition chain of length n, starting with 1 and x. %C A384383 An addition-multiplication-composition chain for the polynomial p(x) is a finite sequence of polynomials, starting with 1, x and ending with p(x), in which each element except 1 and x equals q(x)+r(x), q(x)*r(x), or q(r(x)) for two preceding, not necessarily distinct, elements q(x) and r(x) in the chain. The length of the chain is the number of elements in the chain, excluding 1 and x. %e A384383 An example of a polynomial for which composition is necessary to obtain the shortest chain is 9*x, with the chain (1, x,) 2*x, 3*x, 9*x. (9*x is the composition of 3*x with itself.) So 9*x is one of the 11 polynomials counted by a(3) but not by A384382(3). %Y A384383 Cf. A382928, A383331 (addition only), A384382 (addition and multiplication), A384386, A384482 (addition and composition). %K A384383 nonn,more %O A384383 0,1 %A A384383 _Pontus von Brömssen_, Jun 01 2025