[seqfan] Re: Very nice new sequence A329126 [1, 6, 42, 60, 139810, 126, ...]

[Frank Adams-watters]

Established practice is that such sequences should have the "base" keyword.

Franklin T. Adams-Watters


-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Tue, Nov 12, 2019 9:32 pm
Subject: [seqfan] Very nice new sequence A329126 [1,6,42,60,139810,126,...]

A new sequence sent in by Alon Ran, A329126,
which starts 1, 110, 101010, 111100, 100010001000100010, 1111110,

a(n) is defined to be the lex. earliest string of numbers such that when
read in every base b >= 2, a(n) is divisible by n.

It follows from the definition that all the digits are 0 and 1.  The author
gives a number of other remarks, but it was not completely clear to me
which were empirical observations and which were theorems. I do not have
time to work on it, but it looks like a lovely problem. He gives 21 terms.

The strings are huge. If they are rewritten in base 10 you get A329000
= 1,6,42,60,139810,126,..., which makes it a lot easier to remember the
first few terms.

I hope someone will look into this and figure out what is going on.

It has keyword "base", but it does not depend on any one base - it depends
on all bases (so maybe that keyword is not justified).

Neil

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