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

1,1

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

Links

Table of n, a(n) for n=1..40.

Walter Robinson, Python Program

Example

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.

Prog

(Python) # See Robinson link.

Crossrefs

Cf. A043537, A362769.

Sequence in context: A023075 A084918 A235719 * A057370 A057421 A074211

Adjacent sequences: A365580 A365581 A365582 * A365584 A365585 A365586

Keyword

nonn,base

Author

Valentin Miakinen and Walter Robinson, Sep 20 2023

Status

approved