[seqfan] Re: nice base-dependent sequence

Douglas McNeil mcneil at hku.hk
Mon Jun 7 17:08:29 CEST 2010


> Hugo, Douglas, Zak,   Note the current b-file for A177834 (from Robert Gerbicz)
> has 102 terms.

I'd noticed, and was suitably impressed.  And happy that we agreed on
the lower ones. :^)

Actually, that reminds me.  At the cost of revealing once again that
I'm a bear of very little brain, I don't follow Mr Gerbicz's
description of his sieve, which seems to work beautifully:

> I've used a sieve method to generate the sequence much faster than brute
> force: find n in the form n=100*x+y, where 0<=y<100 so at once we examine
> 100 numbers, let x is given, if you fix a string in n and you want to
> determine the y values for that d|100*x+y, then these y values are in (some)
> arithmetic progressions.

What about "internal" divisors generated by (say) the last four digits
of x and the first digit of y?  I don't see how you'd know which
divisors live directly in the full term "100*x+y" and which live in
the overlapping subterms created by concatenating x and y.  Or am I
misunderstanding "fix[ing] a string in n"?  I fell back to brute force
because unlike a lot of base-related sequences where it's easy to
construct larger terms from smaller terms, here the possibility of
internal divisors defeated me utterly, so I'd like to understand what
I'm missing.  It would probably be useful for many other sequences.


Department of Earth Sciences
University of Hong Kong

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