4
votes
0answers
73 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
0
votes
0answers
19 views

Pattern embedding method

There are three defined functions; $a_n=A(n), b_n=B(n), c_n=C(n)$ and an unknown function $d_n=D(n)$. It has been found out that $d_1=a_1$$d_2=b_1$$d_3=c_1$$d_4=a_2$$d_5=b_2$..... Is there a method ...
9
votes
2answers
157 views

Has anyone noticed this pattern?

I've been messing around a bit and I noticed a curious pattern when it comes to progressions of powers. Let's take the progression of consecutive integers: $1,2,3,4,5,6,7,...$ Obviously it's an ...
3
votes
3answers
139 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
97 views

Some questions about $\gcd(n,m)$ and $\phi(n)$

I was messing around in Excel at the end of work today and made a table where the $(i,j)$ entry $a_{i,j}$, for $j \geq i$, is 1 exactly when $i$ and $j$ are coprime (see snapshot of a portion of the ...
9
votes
7answers
2k views

Pattern to last three digits of power of $3$?

I'm wondering if there is a pattern to the last three digits of a a power of $3$? I need to find out the last three digits of $3^{27}$, without a calculator. I've tried to find a pattern but can not ...
3
votes
0answers
220 views

Pattern puzzle help

I've spent hours on this puzzle, which shouldn't be too hard, and I'm sure I've got the right answer, but apparently it's wrong. The problem statement: You are guessing a positive number X. You ...
0
votes
1answer
139 views

Trying to figure out the pattern in this series

I'm trying to figure out the rule that's producing the series below. The first column is the factorials $1!,2!,3!,4!,5!,6!$ But I can't figure out what else is going on. So I know the next row will ...
7
votes
3answers
744 views

How to find pattern in $1,2,8,9,15,20,26,38…$ infinite sequence?

While I was investigating some specific types of prime numbers I have faced with the following infinite sequence : $1,2,8,9,15,20,26,38,45,65,112,244,303,393,560,....$ I tried to find recursive ...
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) ...