A076697

[Robert Israel]

Can anybody make sense of A076697?  The Name is

Next-to-largest factor of Lucas(n).

Data is

0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 26, 31, 37, 41, 47, 53, 61, 68, 71, 79, 86, 113, 136, 164, 172, 178, 218, 229, 239, 262, 278, 284, 307, 313, 328, 353, 373, 436

But, whether Lucas(n) is supposed to be A000032(n) or A000204(n), these are generally not factors of Lucas(n), let alone the next-to-largest factor.  In fact, there are no Lucas numbers at all divisible by 5, 8, 13, ....

Cheers,

Robert

[Daniel Mondot]

Is there any way to search for large numbers (often buried in b-files) on OEIS?

Google AI tells me that Google has downloaded all .txt files from OEIS, and would find a number, but that's true. I picked a random 13 digit number from a b-file, searched for it, and google didn't find it.

Also, more recently google reports pages where the requested item isn't actually there.

I think that since Google added some AI features in their search, it has been hallucinating results.

Daniel

[D. S. McNeil]

Disclaimer: did this while procrastinating on an errand, but maybe this is meant to be "indices at which new record largest prime factors of Lucas number occur"?  If you squint you can almost see how you'd get the name of the current sequence after some truncation and some corruption.

If so, I match most of the values up to 200 (except +76,-178), and I'm too lazy to wait and/or check factordb for the others.

Doug

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[D. S. McNeil]

Actually it's even better than that, because I can't read: 178 _is_ a new record, so the only discrepancy < 200 is the missing 76.

Doug

[M F Hasler]

On Wed, Apr 9, 2025 at 1:52 PM D. S. McNeil <dsm...@gmail.com> wrote:

Actually it's even better than that, because I can't read: 178 _is_ a new record, so the only discrepancy < 200 is the missing 76.

right, the next missing term was 202, and 239 was to be deleted.

Using my newly contributed PARI code and the b-file for A79451 (= greatest prime factor of A32(n) *) 

I extended the sequence up to all terms < 1000.

and put a meaningful definition and Xrefs to the mentioned sequences and subsequence A1606 = indices of prime Lucas numbers,

and a link to this discussion.

-Maximilian

* side note for A079451 : should use A6530 which is potentially more efficient than brute-force vecmax(factor(...)[,1])