[seqfan] A093553 (and A074200)

hv at crypt.org hv at crypt.org
Mon Jun 24 04:37:10 CEST 2013


After some searching, I found these sequences based on the first 3 terms.

1. When paging through the search results, the page numbers are small and
hard to click on. I've often felt it would be helpful to have "Next" and
"Prev(ious)" buttons - they'd be easier to hit accurately simply by being
wider.

2. First comment on A093553 says "See [A074200] for more information
and further terms". There aren't any further terms there (and the
additional information is minimal).

3. Second comment on A093553 says "It is obvious that this sequence is
increasing and each term is prime. If n>3 then a(n)==1 (mod 10)."

Is "increasing" the same as "strictly increasing", or the same as
"non-decreasing"? I read it as the former, which isn't obviously true
to me: it seemed perfectly plausible that a(4) and a(5) might coincide,
until I saw the actual values here.

The additional comment is also true but misleading: I think the intent
is to highlight that each subsequent term ends in a 1 in decimal,
but we have the much stronger a(n) == 1 (mod 120) for n >= 4: generally
we need a(n) == 1 (mod k_n) where k_n is divisible at least by
2 lcm(1, 2 ... n), and also by n+1 whenever n+1 is prime.

4. Where two sequences are so closely related, it seems less useful to
maintain independent sets of comments, references etc. It might be
better to have the later one say just "A074200+1, see that sequence for
details", and keep all the editing in one place. Even better would be
for the system to support that, so that adding or correcting terms
in the source would automatically propagate corresponding changes to
the derived version.

5. It would have helped me search if there were a way to specify
a) find 2,3,13 only at the start of the sequence; b) I know that the
next term is more than 4800. (Maybe there are ways to do one or both
of those, but I couldn't see them on the search hints.)

But hey, I did find it: the system works. :)

Hugo


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