A378758 Number of 1's required to build n using +, -, and ^.

1, 2, 3, 4, 5, 6, 6, 5, 5, 6, 7, 8, 9, 8, 7, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 7, 6, 7, 8, 9, 8, 7, 8, 9, 9, 8, 9, 10, 11, 12, 12, 13, 12, 13, 12, 11, 10, 9, 8, 9, 10, 11, 12, 12, 12, 12, 13, 13, 12, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 13, 13, 12, 12, 13

Offset: 1

Author

Jake Bird, Dec 06 2024

Keywords

• nonn

Comments

All intermediate steps in building the number should be integers as well, for consistency with related sequences.

A348262(n) >= a(n) >= A091334(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 A091334.

Examples

			a(22) = 10 because 22 = (1+1+1+1+1)^(1+1)-(1+1+1), which has 10 occurrences of the symbol "1", and there is no way of making 22 with fewer using these rules.
Note that A348262(22) = 12 because 22 = (1+1)^(1+1)^(1+1)+(1+1)^(1+1)+1+1; subtraction allows for two fewer occurrences of the symbol "1" to be used here. Similarly, A091334(22) = 9 because 22 = ((1+1+1)^(1+1)+1+1)*(1+1); multiplication allows for one fewer occurrence of the symbol "1" to be used there. 22 is the least n such that A348262(n) > a(n) > A091334(n).
		

Links

• Jake Bird, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000027 {1,+}, {1,+,-}

Cf. A005245 {1,+,*}

Cf. A348262 {1,+,^}

Cf. A091333 {1,+,-,*}

Cf. A025280 {1,+,*,^}

Cf. A378759 {1,+,/,^}

Cf. A091334 {1,+,-,*,^}

Cf. A348089 {1,+,-,*,/,^}