关于p进制下最右侧非最大基数数字的指数索引的标准命名问询

Hey there! I totally get what you're trying to pin down here—you're looking for a standard, agreed-upon name for that index pointing to the rightmost digit (in any base p) which isn't equal to p-1 (the maximum possible digit for that base). Let's start by grounding this with your examples to make sure we're aligned:

• In base 10, take the number 8243848392842992999: the rightmost non-9 digit sits at the 10^3 place, so your target index is 3.
• In base 3, for the number 0120120220220212211112 (written in base 3), the rightmost non-2 digit is at the 3^1 place, so the index is 1.

Now, to answer your core question: there isn't a single, universally accepted standard name for this specific index that's used across all areas of math or computer science. That said, there are some related concepts and clear descriptive phrases you can use, depending on context:

1. Divisibility-based equivalent: This index is exactly equal to the highest power of p that divides n + 1 (where n is your original number). Let's test this with your examples:

   • For your base-10 number a, a + 1 ends with three 0s, meaning 10^3 divides a + 1 but 10^4 doesn't—so the exponent here is 3, which matches your index.
   • For your base-3 number b, b + 1 would end with a 0 (since the units digit is 2, adding 1 flips it to 0 and carries over to the 3^1 place), so 3^1 divides b + 1 but 3^2 doesn't—again, matching your index of 1.
     This is a formal mathematical way to reference the value, and it's widely understood in number theory problems involving digit patterns or divisibility rules.

2. Descriptive plain-language terms: If you need a more intuitive name (especially for writing code or explaining to non-specialists), phrases like:

   • Rightmost non-maximal digit exponent
   • Trailing maximal digit count (since the index equals the number of consecutive trailing p-1 digits in the number)
     work perfectly well. You mentioned "first nonpenultimate digit"—that's understandable but a bit clunky, so the above phrases are clearer.

If you're creating a formal document, paper, or codebase, the best practice is to define your chosen term explicitly at the start (e.g., "For any integer n in base p, let k(n) denote the exponent of the rightmost digit of n that is not equal to p-1") and then stick with it consistently. This avoids any confusion, even if there's no universal standard name.

备注：内容来源于stack exchange，提问作者tekay-squared