cp's OEIS Frontend

A378759 Number of 1's required to build n using +, /, and ^.

%I A378759 #8 Dec 21 2024 00:51:47
%S A378759 1,2,3,4,5,6,7,5,5,6,7,8,9,9,10,6,7,8,9,10,11,12,13,11,7,8,6,7,8,9,10,
%T A378759 7,8,9,10,8,9,10,11,12,10,11,12,13,13,14,15,13,9,10,11,12,13,12,13,14,
%U A378759 13,14,13,14,12,13,11,7,8,9,10,11,12,13,14,12
%N A378759 Number of 1's required to build n using +, /, and ^.
%C A378759 All intermediate steps in building the number should also be integers.
%C A378759 A348262(n) >= a(n) >= A348089(n) for all n, as the available operators in A348262 are a subset of the available operators here, and the available operators here are a subset of the available operators in A348089.
%H A378759 Jake Bird, <a href="/A378759/b378759.txt">Table of n, a(n) for n = 1..119</a>
%e A378759 a(14) = 9 because 14 = ((1+1+1)^(1+1+1)+1)/(1+1), which has 9 occurrences of the symbol "1", and there is no way of making 14 with fewer using these rules.
%e A378759 Note that A348262(14) = 10 because 14 = (1+1+1)^(1+1)+(1+1)^(1+1)+1; division allows for one fewer occurrence of the symbol "1" to be used here. Similarly, A348089(14) = 8, because 14 = (1+1)^(1+1)^(1+1)-(1+1); subtraction allows for one fewer occurrence of the symbol "1" to be used there. 14 is the least n such that A348262(n) > a(n) > A348089(n).
%Y A378759 Cf. A000027 {1,+}, {1,+,-}
%Y A378759 Cf. A005245 {1,+,*}
%Y A378759 Cf. A348262 {1,+,^}
%Y A378759 Cf. A091333 {1,+,-,*}
%Y A378759 Cf. A378758 {1,+,-,^}
%Y A378759 Cf. A025280 {1,+,*,^}
%Y A378759 Cf. A091334 {1,+,-,*,^}
%Y A378759 Cf. A348089 {1,+,-,*,/,^}
%K A378759 nonn
%O A378759 1,2
%A A378759 _Jake Bird_, Dec 06 2024