A378758 -id:A378758 - cp's OEIS frontend

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

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, 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, 13, 14, 13, 14, 12, 13, 11, 7, 8, 9, 10, 11, 12, 13, 14, 12

Offset: 1

Jake Bird, Dec 06 2024

nonn

All intermediate steps in building the number should also be integers.

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.

			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.
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).

Jake Bird, Table of n, a(n) for n = 1..119

Cf. A000027 {1,+}, {1,+,-}
Cf. A005245 {1,+,*}
Cf. A348262 {1,+,^}
Cf. A091333 {1,+,-,*}
Cf. A378758 {1,+,-,^}
Cf. A025280 {1,+,*,^}
Cf. A091334 {1,+,-,*,^}
Cf. A348089 {1,+,-,*,/,^}

cp's OEIS Frontend

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

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