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 A348089 #14 Dec 06 2024 11:23:30 %S A348089 1,2,3,4,5,5,6,5,5,6,7,7,8,8,7,6,7,7,8,8,9,9,9,8,7,7,6,7,8,9,8,7,8,9, %T A348089 8,7,8,9,10,10,10,11,12,11,10,11,10,9,8,9,10,9,9,8,9,9,10,10,11,11,10, %U A348089 9,8,7,8,9,10,11,11,10,10,9,10,10,10 %N A348089 Number of 1's required to build n using +, -, *, /, and ^. %C A348089 Here division is taken to be strict integer division, i.e., j/k is defined only if k|j. %C A348089 Because of the presence of exponentiation, division reduces the value of a(n) as compared with A091334(n) (which allows the same operations except division) far more often than adding division to A091333 does; see A348069. %H A348089 Glen Whitney, <a href="/A348089/b348089.txt">Table of n, a(n) for n = 1..3802</a> %H A348089 Glen Whitney, <a href="/A348089/a348089.py.txt">Python3.8 program to compute a(n) for some values of n</a> %e A348089 Because 41 = ((1+1+1)^(1+1+1+1) + 1)/(1+1), and there is no expression with these operators and fewer ones that evaluates to 41, a(41) = 10. Note that 41 is the least n such that a(n) < A091334(n). %Y A348089 Cf. A005245 (variant using + and *), A025280 (using +, *, and ^), A091333 (using +, -, and *), A091334 (using +, -, *, and ^), A348262 (using + and ^). %Y A348089 Cf. A348069. %K A348089 nonn %O A348089 1,2 %A A348089 _Glen Whitney_, Sep 28 2021