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 A354914 #28 Apr 12 2025 09:42:50 %S A354914 0,1,2,1,2,2,3,1,2,2,3,2,3,3,3,1,2,2,3,2,3,3,4,2,2,3,2,3,3,3,3,1,2,2, %T A354914 3,2,3,3,3,2,3,3,3,3,3,4,4,2,3,2,3,3,4,2,3,3,3,3,3,3,4,3,3,1,2,2,3,2, %U A354914 3,3,4,2,3,3,3,3,4,3,4,2,2,3,3,3,3,3,3,3,3,3,3,4,3,4,4,2,3,3,3,2 %N A354914 The least cost to reach n using additions and multiplications, where multiplication is free. %C A354914 Start with 1. Apply multiplication or addition to any values (not necessarily distinct) already attained to get a finite sequence of integers ending in n. The cost of addition is one unit, but multiplication is free. Then a(n) is the cost of the least expensive path to n. %C A354914 The problem is folklore. It is not hard to prove that the cost function is unbounded. The values given were produced by Joseph DeVincentis, Stan Wagon, and Al Zimmermann. %H A354914 Stan Wagon, <a href="/A354914/b354914.txt">Table of n, a(n) for n = 1..5000</a> %H A354914 H. M. Bahig, <a href="http://dx.doi.org/10.1016/j.disc.2007.04.015">On a generalization of addition chains: Addition-multiplication chains</a>, Discrete Mathematics 308 (2008), 611-616. %H A354914 Stan Wagon, <a href="/A354914/a354914.txt">Optimal paths for n up to 100</a> %e A354914 For n = 23, the least cost a(23) is 4, via the sequence 1, 2, 3, 4, 8, 16, 19, 23. %Y A354914 Cf. A355015, A230697. %K A354914 nonn %O A354914 1,3 %A A354914 _Stan Wagon_, Jun 11 2022