[seqfan] Re: A mysterious sequence from Russia

[Allan Wechsler]

My Russian is fairly rudimentary, but I'm getting something like:

"Let 1/p = 0.(a_1...) and let us have the period (a_1 ... a_k), we
understand/interpret(?) that the number a_1...a_k (as a natural [number],
without the leading decimal point) equals (10^n-1)/p from the first ... "

So the submitter is considering the repeat-block of some reciprocal, read
in decimal, as a number.

It is annoying that Wiktionary does not have separate entries for the
different case-forms of Russian nouns and adjectives.


On Fri, Feb 28, 2014 at 1:56 PM, Neil Sloane <njasloane at gmail.com> wrote:

> I have a friend who collects abandoned
> computers from the town dump. I sometimes look for sequences in the OEIS
> trash heap of abandoned sequences.
>
> Here is one such:
>
> Question: what is this sequence?
>
> 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 3, 6, 3, 0, 3, 6, 4, 285700, 4,
> 5, 4, 846200, 4, 5, 4, 5, 4, 363600, 3, 6, 4, 5, 4, 153800, 4, 170700, 4,
> 5, 4, 5, 4, 5, 4, 5, 4, 245300, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5
>
> Source: an abandoned version of A230604 (see the "history")
>
> Hints (from the "history"):
>
> 1/N = 0,(a_1a_2a_3a...a_n)
>
> k= S/n
>
> There are two kinds of N. The first one is: the length of the period is an
> even and k is 4.5. The second- where the length is odd.
>
> The improve:Пусть 1/p = 0,a_1a_2a_3...И пусть у нас есть период
> (a_1a_2a_3...a_k)Поймём, что число a_1a_2...a_k (уже натуральное, без
> ведущей десятичной запятой) равно (10^n - 1) / p для первого    ... (long
> text follows)
>
> Example: If N is 7,1/7=0.(142857)
>
> S=1+4+2+8+5+7=27
>
> n=6
>
> k=4.5
>
> This suggests that this is really a sequence of fractions: 9/2, 9/2, ....
> but what is the real definition?
>
> This may or may not be an interesting sequence. Maybe someone who reads
> Russian could take a look . This is such a classical part of elementary
> number theory that it is unlikely to be new. But one never knows.
>
> Neil
>
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