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February 3

About lucky numbers

If x is a lucky number and n is a natural number, must there be infinitely many lucky numbers == x mod n? Is there an analog of Dirichlet's theorem on arithmetic progressions to the lucky numbers rather than the prime numbers? 210.244.72.152 (talk) 02:57, 3 February 2024 (UTC)[reply]

Funny enough, while looking for information on lucky number congruences online, I found a Math StackExchange answer that mentioned this very question. Unfortunately, as it stands, it appears to yet be unsolved. GalacticShoe (talk) 05:48, 3 February 2024 (UTC)[reply]

Note that the author of this answer (as mentioned within the answer itself) has a paper (archived here) where it is proven that each iteration of the lucky sieve removes certain sets of congruences. Although this is not enough to show that some congruences are never touched and thus infinite, it does at least show that there is some method to the lucky sieve madness. GalacticShoe (talk) 05:53, 3 February 2024 (UTC)[reply]

Always nice...

When you try to put together a question here, spend a minute or two trying to describe, write out the values that you've figured in the sequence and then find it in an oeis search. (A006561 Number of intersections of diagonals in the interior of a regular n-gon.). Sort of surprised that the answer is as clean as it is for odd numbers, but as dirty as it is for even.Naraht (talk) 03:19, 3 February 2024 (UTC)[reply]

Agreed, although conversely I find it rather disappointing when I generate the first few terms and there is no sequence instead. On the one hand, uncharted waters are cool, but on the other hand, they're kinda scary too. GalacticShoe (talk) 05:17, 3 February 2024 (UTC)[reply]

If it is an interesting sequence, submit it to OEIS. Bubba73 ^{You talkin' to me?} 05:47, 3 February 2024 (UTC)[reply]

Good idea, although unfortunately I highly doubt that any of the sequences I come up with are interesting or particularly novel. GalacticShoe (talk) 05:56, 3 February 2024 (UTC)[reply]

I think they just need to be good enough to start talking to somebody else about. They've lots of room. NadVolum (talk) 12:26, 4 February 2024 (UTC)[reply]