[seqfan] A mysterious sequence from Russia

Neil Sloane njasloane at gmail.com
Fri Feb 28 19:56:19 CET 2014


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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