A348089 Number of 1's required to build n using +, -, *, /, and ^.

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, 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, 9, 8, 7, 8, 9, 10, 11, 11, 10, 10, 9, 10, 10, 10

Offset

1,2

Comments

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

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.

Links

Glen Whitney, Table of n, a(n) for n = 1..3802

Glen Whitney, Python3.8 program to compute a(n) for some values of n

Example

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).

Crossrefs

Cf. A091334, A091333, A348069.

Sequence in context: A154940 A133344 A323727 * A091334 A306560 A025280

Adjacent sequences: A348086 A348087 A348088 * A348090 A348091 A348092

Keyword

nonn

Author

Glen Whitney, Sep 28 2021

Status

approved