A348089 - OEIS

%I #11 Oct 05 2021 08:25:08

%S 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 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 9,8,7,8,9,10,11,11,10,10,9,10,10,10

%N Number of 1's required to build n using +, -, *, /, and ^.

%C Here division is taken to be strict integer division, i.e., j/k is defined only if k|j.

%C 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 Glen Whitney, <a href="/A348089/b348089.txt">Table of n, a(n) for n = 1..3802</a>

%H Glen Whitney, <a href="/A348089/a348089.py.txt">Python3.8 program to compute a(n) for some values of n</a>

%e 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 Cf. A091334, A091333, A348069.

%K nonn

%O 1,2

%A _Glen Whitney_, Sep 28 2021