2
votes
0answers
67 views

Unexplanied pattern from increasing rational sequences

I've stummbled upon some strange pattern when working with series of rational numbers. If anyone could shed light on this phenomenon I will be most greatful. Backgroud: Working in an integer lattice ...
0
votes
0answers
78 views

Number of differently-sized squares needed to fill a rectangle; is there a visible formula? [Pattern spotting]

Consider a game in which we tile a given rectangle with the largest squares that will fit. We record the number of squares of each size that we can use, until the rectangle is completely covered. ...
3
votes
3answers
137 views

Largest number on multiplying with itself gives the same number as last digits of the product

What is the largest number on multiplying with itself gives the same number as last digits of the product? i.e., $(376 \times 376) = 141376$ i.e., $(25\times 25) = 625$ If the largest number cant ...
3
votes
1answer
71 views

finding all pairs $(x,z)$

How to find all pairs $(x,z)$ of integers for which $2(z+1)^3$ is divisible by $xz-1$
1
vote
3answers
316 views

Patterns in Sequences

I've heard in a movie that for any sequence of numbers, there is a nice formula for generating that sequence. So, for example if I write: 1,2,1,2,3,3,1,2,3,1,2,4,... There is a formula for ...
0
votes
3answers
1k views

Extract a Pattern of Iterated continued fractions from convergents

I have been working on an article at https://oeis.org/wiki/Table_of_convergents_constants where I posted a table of "convergents constants" (defined at https://oeis.org/wiki/Convergents_constant) ...