AIME II 2026 (Problem 4)

For each positive integer

n

let

f(n)

be the value of the base-ten numeral

n

viewed in base

b

, where

b

is the least integer greater than the greatest digit in

n

. For example, if

n=72

, then

b=8

, and

72

as a numeral in base

8

equals

7\cdot8+2=58

; therefore

f(72)=58

. Find the number of positive integers

n

less than 1000 such that

f(n)=n