# Talk:Magic numbers

## Not magic?

A144688 defines Magic numbers: "all numbers from 0 to 9 are magic; a number >= 10 is magic if it is divisible by the number of its digits and the number obtained by deleting the final digit is also magic." So 1 is not Magic because 1 divides 1.--Nigel Galloway (talk) 13:18, 10 February 2023 (UTC)

- Alternatively, we might focus on the tension between the opening statement "Magic numbers are polydivisible numbers in base 10. A polydivisible number is a number where the first n digits are evenly divisible by n" and the later statement "There is a finite number of magic numbers.". (If n=1, all positive integers would be magic numbers, if n=2, half of all positive integers would be magic numbers, etc.)

- Anyways, it's clear that the current task description does not match the referenced OEIS:144688 sequence. --Rdm (talk) 13:29, 10 February 2023 (UTC)

- (In response to Nigel Galloway) "...1 is not Magic because 1 divides 1." Perhaps not, but
*effectively*they may be thought of as being that, because they are magic whether you treat them as being evenly divisible by one or just summarily declare them to be magic. Saying they are magic because "the first n digits are evenly divisible by n" is more defensible than "because I said so" in my opinion. --Thundergnat (talk) 16:26, 10 February 2023 (UTC)

- (In response to Rdm) "If n=1, all positive integers would be magic numbers" False. If n = 1 then all
**single digit**positive integers would be magic. And they are. "if n=2, half of all positive integers would be magic numbers" False again. If n=2, half of all**two digit**positive integers would be magic numbers. And they are. "it's clear that the current task description does not match the referenced OEIS:144688 sequence." In what way? They both contain the same number of values, in fact, consist of the exact same values. In what way do they differ? --Thundergnat (talk) 16:26, 10 February 2023 (UTC)

- (In response to Rdm) "If n=1, all positive integers would be magic numbers" False. If n = 1 then all

- The OEIS page definition seems to me to be equivalent to the definition on the task page. The OIES page makes explicit that the number with the final digit removed must also be magic (requiring special treatment of the single digit numbers), but that is implicit in the task definition. Explicitly stating the final digit removal must result in a Magic Number is possibly a hint of a way to how to solve the task. --Tigerofdarkness (talk) 20:56, 10 February 2023 (UTC)