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