A365583 Numbers k with property that k can be represented by the digits present in k using the operations specified in the comment, and requiring fewer digits than the number of digits in k.

1024, 1253, 1287, 1296, 1331, 2048, 2163, 2187, 2435, 2500, 2564, 2568, 2916, 3025, 3125, 3216, 3375, 3437, 3645, 3729, 4088, 4096, 4256, 4375, 4625, 5129, 5243, 6250, 6254, 7128, 7293, 7343, 7776, 8256, 9025, 9216, 9375, 9512, 10003, 10004

Offset: 1

Author

Valentin Miakinen and Walter Robinson, Sep 20 2023

Keywords

• nonn
• base
• changed

Comments

The only operations allowed are addition, subtraction, multiplication, division, exponentiation, parenthesizing, and concatenation.

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 k = 3125, k can be represented as 5^5, using only 2 digits, which is less than the length of k, 4.
For k = 3437, k can be represented as (7^3)||7, using only 3 digits which is less than the length of k, 4.
For k = 10003, k can be represented as ((1||0)^3)||3, using only 4 digits, which is less than the length of k, 5.
		

Links

• Walter Robinson, Python Program

Crossrefs

Cf. A043537, A362769.

Programs

Python

# See Robinson link.