A362769 Minimum number of digits required to represent n only using digits present in n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 7, 4, 4, 4, 3, 5, 5, 4, 3, 5, 6, 6, 4, 3, 2, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 2, 4, 4, 4, 5, 5, 5, 4, 5, 3, 4, 5, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 3, 4, 3, 4, 4, 5, 5, 4, 5, 5, 5, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 5, 5, 4, 5, 5, 5, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 9

Offset: 1

Author

Oskar Macholl, Valentin Miakinen, and Walter Robinson, May 02 2023

Keywords

• nonn
• base
• changed

Comments

The only operations allowed are addition, subtraction, multiplication, division, exponentiation, and parenthesizing. Concatenation is not allowed.

Real and imaginary intermediate values are allowed as long as the final value of the expression is an integer. - Walter Robinson, Aug 22 2025

Examples

			For n = 10, a solution for a(10)=6 is (1+1+1)^(1+1)+1.
For n = 27, a solution for a(27)=4 is 2+(2-7)^2.
		

Links

• Valentin Miakinen, Python program

Crossrefs

Cf. A043537.

Programs

Python

# See Miakinen link.

Extensions

Edited by N. J. A. Sloane, Oct 16 2023.