[seqfan] Re: Very nice new sequence A329126 [1, 6, 42, 60, 139810, 126, ...]
David Seal
david.j.seal at gwynmop.com
Thu Nov 11 17:30:48 CET 2021
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I suspect the current wording arose because the sequence isn't really a sequence of integers, but a sequence of representations of integers. E.g. if the sequence is read in base 2, it is the sequence of integers (represented in decimal):
1, 6, 42, 60, 139810, 126, ...
but if read in base 3, it is the sequence of integers (represented in decimal):
1, 12, 273, 360, 130754415, 1092, ...
and if read in base 4, it is the sequence of integers (represented in decimal):
1, 20, 1092, 1360, 17247241220, 5460, ...
etc. So "a(n) is the least positive integer which yields a multiple of n when read in any base" isn't accurate because you don't read integers in bases, but instead read digit strings in bases. But I agree that the current wording, while recognising that fact, made a worse mistake with "lexicographically earliest"...
I think it needs something like "the least positive integer whose decimal representation can be read in any numeric base (so consists of only 0s and 1s) and always yields a multiple of n when read in any numeric base".
David
> On 09/11/2021 06:34 Don Reble via SeqFan <seqfan at list.seqfan.eu> wrote:
> ...
> > %S A329126 1,110,101010,111100,100010001000100010,1111110
> > %N a(n) is the lexicographically earliest string of digits which
> > yields a multiple of n when read in any numeric base.
>
> Does the author really mean "lexicographically earliest"?
> There are many candidates for a(2): 110, 1010, 10010, 100010, ...,
> Each is divisible by 2 in any base. Lexicographically,
> each is earlier than the previous, and there is no earliest.
>
> I think he means simply "the least positive integer which yields
> a multiple...".
> ...
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