# Talk:Construction of Smith Number from Prime Repunit

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$3304$ is not the smallest multiplier.

According to https://primes.utm.edu/glossary/page.php?sort=SmithNumber, we have a list of multipliers, smallest of which is $1540$.

The webpage has made no claims on whether $1540$ is the smallest working multiplier.

(Curiously the webpage does not list $3304$ even though it works.)

$3304$ could be the smallest multiplier that gives the digit sum $n + 27$?

It shouldn't be hard to crunch through a few thousand numbers, so I will give it some thought. --RandomUndergrad (talk) 05:14, 7 March 2022 (UTC)

- Or find the sequence on OEIS: This sequence is A104167 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

- --RandomUndergrad (talk) 06:01, 7 March 2022 (UTC)

- Yep, it's added to the list of errata (not that it really was an erratum when Wells wrote it). --prime mover (talk) 06:04, 7 March 2022 (UTC)

- Oh, and don't trust the OEIS sequence, it is just a copy of the above website and does not include $3304$. The field is wide open for research.

- Do you have an account set up on OEIS? --prime mover (talk) 06:06, 7 March 2022 (UTC)

- I think it is the other way round: the website took an exerpt from the OEIS sequence (the OEIS sequence has 1000 terms).

- $3304$ was excluded because it does not work for $R_n = 11$; all other numbers in the sequence works for $11$ as well, as remarked in the comments of that sequence.

- On an unrelated note, I do have an account there. --RandomUndergrad (talk) 06:28, 7 March 2022 (UTC)

- Sorry, yes of course. I wasn't paying attention. --prime mover (talk) 07:26, 7 March 2022 (UTC)