A348262 Number of 1's required to build n using + and ^.

1, 2, 3, 4, 5, 6, 7, 5, 5, 6, 7, 8, 9, 10, 11, 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, 12, 13, 12, 13, 13, 14, 15, 13, 9, 10, 11, 12, 13, 12, 13, 14, 14, 14, 13, 14, 15, 16, 14, 7, 8, 9, 10, 11, 12, 13, 14, 12, 12, 13, 14, 15, 16, 17

Offset: 1

Author

Glen Whitney, Oct 09 2021

Keywords

• nonn

Examples

			11+111++^ is a minimal-length RPN formula with value 8, using just these operators. It contains five occurrences of the symbol "1". Hence, a(8) = 5.
		

Links

• Glen Whitney, Table of n, a(n) for n = 1..10000
• Edinah K. Ghang and Doron Zeilberger, Zeroless Arithmetic: Representing Integers ONLY using ONE, arXiv:1303.0885 [math.CO], 2013.
• Glen Whitney, Python3.8 program to compute a(n)
• Index to sequences related to the complexity of n

Crossrefs

Cf. A213924 (expression-length complexity with the same set {1,+,^}).

Cf. A005245 (variant using + and *), A025280 (using +, *, and ^), A091333 (using +, -, and *), A091334 (using +, -, *, and ^), A348089 (using +, -, *, /, and ^).

Formula

a(n) = (A213924(n) + 1)/2.