1. From a samples of a small samples of mathematical objects, conjecture a common pattern to all of them. This includes "guess the next terms in the sequence" question (consider checking OEIS first). Please provide as much context as possible. 2. Mathematical ideas related to pattern recognition, ...

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-2
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2answers
62 views

Cant find the pattern [on hold]

These are two sequences: I tried looking for a ratio or difference but it wasnt working $$ 12,20,32,\underline{\quad},22,\underline{\quad},50 $$ $$ 6,10,16,8,\underline{\quad},22\underline{\quad} $$ ...
0
votes
0answers
15 views

Lower bound of Nearest Neighbour Rule

It is stated often as a matter of fact that the lower bound for Nearest Neighbour rule is the Baye's rate. However when I tried to mathematically prove it,I hit a dead end. For reference : Error for ...
1
vote
0answers
59 views

How can a pattern be found in a series of Numbers?

In the given series of numbers (0-9) or a similar series of numbers, How can a pattern be searched? 3 2 4 8 0 8 7 3 8 7 0 0 4 9 6 3 9 7 4 5 7 3 9 6 ...
0
votes
2answers
47 views

Is there a general expression for this pattern?

I am trying to find a general expression for this pattern, I know it must be something stupidly easy but I can't seem to find it. Could somebody please help me?
0
votes
1answer
24 views

Quadratic number pattern equation

May I know how do I form a quadratic number pattern equation? I cant seem to form one on my own. 1500, 1519,1536, 1551,1564.
1
vote
1answer
44 views

Sequence patterns

Hi I'm new and I was wondering if a pattern could be derived from this. I wrote a program which printed all the numbers up until a number the user inputted, and then continuously deleted the middle ...
0
votes
0answers
15 views

Where do I need to use regularization parameter lambda for better results?

In polynomial curve fitting problem as below, if $y(x,w)$ is the output when $x$ is the input vector, $w$ are the coefficients and and $M$ is the order of polynomial.. And if $t_n$ is the target ...
9
votes
1answer
92 views

Relationship between primes and practical numbers

This is my first post here. I am a musician, and not a mathematician, but I enjoy doing things to prime numbers and seeing what comes out. I have defined a sequence which takes the following values ...
-8
votes
3answers
151 views

Interesting patterns to the algebraic solutions of polynomials [closed]

In yet another attempt to find the solution to the quintic polynomial, I started looking backwards at the solutions to the quartic, cubic, quadratic, and linear polynomials to see if I could pick up ...
1
vote
0answers
57 views

Did the U.S. Army use a formula to evaluate fitness performance?

While writing a web app to calculate one's score on the Army Physical Fitness Test (APFT), I grew tired of simply retyping this chart: ...
0
votes
2answers
59 views

Find the number to replace the question mark in between two pairs of numbers

Here is the problem: I have to find the number to replace the question mark. I know there is a series or a pattern to find it any hint will be very helpful.
2
votes
3answers
66 views

Is there a way of making “guess the next number in the sequence” rigorous?

This is maybe more of a question for matheducators.SE than math.SE but I'm more interested in the math than the education. A common problem given to middle and high school kids (at least in America) ...
6
votes
1answer
158 views

Please, help to identify this numerical constant

I'm trying to find an answer to this question. Let $K(k)$ be the elliptic integral of the first kind and $K'=K(\sqrt{1-k^2})$. According to Abel's theorem (see this link) we know that if ...
1
vote
3answers
54 views

Is there a pattern to the golden ratio number figures?

The golden ratio or phi is 1.6180339887498948482045... I am wondering if there is a pattern in the numbers so given a certain set of figures, you are able to figure out the rest of the figures ...
3
votes
1answer
48 views

Fibonacci-Like Sequence: Breeding Rabbits

I came across the following question on a math test: Suppose Fibonacci's research in the breeding habits of rabbits has been adjusted. They are now believed to be fertile after $2$ months of life, ...
5
votes
2answers
400 views

Has anyone seen this pattern that evaluates to $-\frac{1}{3}$ always?

I was recently doodling and came upon an interesting pattern. Beginning with $0$, add $1$, subtract $2$, divide by $3$, and multiply by $4$. Then add $5$, subtract $6$, divide by $7$, and multiply by ...
0
votes
2answers
47 views
-2
votes
1answer
47 views

How to find the 999th shape in a pattern?

The pattern is of a triangle followed by 3 stars and 4 circles and it continues to repeat. What will the 999th shape in the pattern be? Explain how you can tell.
0
votes
0answers
25 views

Usefulness of Finding Patterns

I have been working trying to find different sequences and series with particular patterns of numbers. I was wondering, however, what the use of finding different patterns in these numbers has? Is ...
0
votes
0answers
11 views

Patterns in the Ulam Spiral

Is anyone familiar with work that has been done finding patterns in the Ulam Spiral? For instance, if I picked a random number in the spiral, and then picked a diagonal radiating outward, what would ...
1
vote
1answer
37 views

Function for numeric input output series

I am trying to find function which will give me output for corresponding inputs. ...
0
votes
1answer
25 views

Determining the pattern in a basic numerical series

In the context of finding the series solution for a variable coefficient ODE, I have to determine if a consistent pattern exists between the following numbers: $\frac{-1} {3!},\frac{-1} ...
0
votes
2answers
182 views

Find a formula for the sequence 1,3,6,10,15,…

Write a formula/formulae for the following sequence: b). 1,3,6,10,15,... I am not getting any pattern here, from which to derive a formula. This sequence does not look like the examples I ...
0
votes
2answers
52 views

Finding the general term of a sequence (if there's any)

I would like to know if it's possible to find an expression for the following sequence $\;\{a_n\},\;n=0,\,1,\,2,\,3,\,\dots\;$ $1, 3 , 7, 13, 21...$ Someone would like to explain me what I have to ...
0
votes
1answer
69 views

State machine scenario: finding invariant

Alice, Bob, and Charles want to evenly distribute a dozen doughnuts. Initially, Alice has 5, Bob has 3, and Charles has 4. However, they want to do it according to the following rules: 1) Bob may ...
-2
votes
2answers
53 views

Find mising numbers from a sequence 1,4,?,16,?,36,? [closed]

Please help me find the number absent in the line for the follow sequence $1,4,?,16,?,36,?$. For example I know the absent number in the sequence $5,0,-5,\_,\_,$, they are $-15,-20$. But I didn't ...
0
votes
1answer
22 views

how to find formula that matches pattern

I have a pattern that I'm struggling to find the formula for. For inputs of 0 - 3, the expected result is 0. For inputs 4 - 6, the expected result is 3. 7 - 9 should output 6. 10 - 12 should output ...
0
votes
3answers
32 views

Sum of Odd Numbers make Squares

Look at this: 1 (+3) 4 (+5) 9 (+7) 16 (+9) 25 (+11) 36 (+13) 49 And so forth, you get the idea. Why do they make up this pattern? And is there any special name for this ...
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votes
1answer
81 views

Find the pattern sequence

I'm trying to help my grandchild with $6$th grade math homework. The question given is: $$ 3.5,\ \ 13,\ \ 41.5,\ \ 127, \cdots $$ What are the next $3$ numbers?
0
votes
3answers
80 views

What's the generating formula for this sequence [closed]

Can someone help me finding the generating formula for this sequence? $$[1,1,3,5,5,7,9,9,11,13,13...]$$ Thanks!
0
votes
1answer
22 views

Help figuring out a simple formula?

I have an alpha value with a range of 0.0 - 1.0 as well as a value N. If the alpha value is 0.5, I want to make no change to N. If the alpha value is 0, I want to double N. If the alpha value is 1.0 I ...
0
votes
3answers
73 views

Is there a way to write $\dots 2(2(2(2+1)-1)+1)-1 \dots$ in closed form?

It's something like a sequence I'm working with and a part of it has coefficients, which go $3$, $5$, $11$, $21$ and so on. I was wondering if it's possible to find a (closed) formula dependent on say ...
5
votes
3answers
344 views

figuring out an integer function

$f(1) = 1\\ f(2) = 2\\ f(3) = 6\\ f(4) = 20\\ f(5) = 70\\ f(6) = 252\\ f(7) = 924\\ f(8) = 3432\\ f(9) = 12870$ Then what is $f(n)$ (where $n > 0$)? I though about many many possibilities but ...
3
votes
2answers
217 views

Finding the general formula of a sequence: $3,8,23,68,203,608,\cdots$

I have the following sequence : $$3,8,23,68,203,608,\cdots$$ I have found that definition by recurrence of this is $$a(n)=3a(n-1)-1$$ where $a_0=3$ as the first term. I want to find the explicit ...
0
votes
1answer
28 views

What is a permutation pattern?

The wikipedia entry for permutation pattern gives this as an example: For example, in the permutation π = 391867452, π1=3 and π9=2. A permutation π is said to contain the permutation σ if there ...
2
votes
1answer
70 views

Is this a valid visualization of Euler's identity as a more generic pattern?

I was reading this nice question about a demonstration of Euler's identity, and tried to visualize how would look the left part of the identity in the complex plane by using the following function: ...
1
vote
0answers
18 views

Anyone know of algorithm for compairing real planar graphs? (for OCR)

The picture pretty much explains it. I will have a collection of line segment graphs to compare against and it's okay if it's $O(n)$ here because the set is the ASCII set or smaller . I was ...
1
vote
1answer
43 views

Understand about maximum a posteriori probability (MAP) in classfication task

I have a 2D image defined on a region $\Omega$. Let $I: \Omega \to R$ be a gray image. Assume that the region can be separated into $N$ sub-regions $\Omega_i$ such that $$\forall i,j=1... N:\Omega_i ...
0
votes
0answers
34 views

What is the Sequence?

for n when n is 1 then it gives 2 n is 2 then it gives 4 n is 3 then it gives 7 n is 4 then it gives 11 How do I write this sequence in equation form?
0
votes
1answer
63 views

Finding patterns in seemingly arbitrary pairs of numbers

I don't work (directly) in mathematics (I'm a programmer), but I see numbers every day. Today I came across an issue where some totals were off, and was sent a list of the last 9 examples of the ...
19
votes
2answers
312 views

What is this pattern found in the first occurrence of each $k \in \{0,1,2,3,4,5,6,7,8,9\}$ in the values of $f(n)=\sqrt{n}-\lfloor \sqrt{n} \rfloor$?

Learning how to generate the Mandelbrot set, I came across the definition of the "escape condition" which is the one that decides the color that is applied to each point of the plane where the ...
1
vote
1answer
71 views

what is the formula for this function?

I've been thinking about the differences in numbers so for example: $\begin{array}{ccccccc} &&&0&&&\\ ...
0
votes
3answers
314 views

Sequence of $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5$

‘A sequence is formed by writing the integers the corresponding number of times as follows : 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, … What is the 800 th term in this sequence?’
0
votes
2answers
113 views

Can't figure it out, why is this answer is right. By what pattern

I found this example in some old book and can't figure it out, why is this answer is right. Would like to get an explanation to it. Thanks in advance. I don't have reputation over 10, so I uploaded ...
0
votes
3answers
113 views

How do I solve the missing number in a series using the application of calculus?

5,6,10,19,35, ... I know the way to solve this with the basic way i.e. finding the difference. Otherwise, look for the square and difference since the number is growing kind of exponentially. ...
1
vote
2answers
48 views

Is there a obvious pattern between a Catalan number and another?

I know that $ C_n = C_0 C_{n-1} + C_1 C_{n-2} + C_2 C_{n-3} + \cdots + C_{n-1} C_0 $., but I was wondering if there was a more obvious pattern between $C_n$ and $C_{n+1}$.
-3
votes
1answer
43 views

What is the member in the last set of this pattern? [closed]

(42,15,3) (24,20,2) (?,12,4) ? indicates the number I do not know
2
votes
1answer
48 views

Derive a formula for the number of small square base pyramids required to create a bigger pyramid?

To quote from the problem statement: "Pyramids are built using smallest pyramids of "level 1", that are used as building blocks for higher levels. Stacking pyramids of "level 1" to create ...
0
votes
0answers
71 views

Is there a pattern that can be seen in this sequence?

I can't seem to find any pattern, perhaps a fresh view from one of you guys can point me to the right direction: 14898997873, 16483634594, 17241926510, 16427260053, 19933377255, 7467660818, ...
11
votes
3answers
292 views

Digital root of twin prime semiprimes

It appears that the product of any pair of twin primes (excluding the first pair 3 and 5) yields a semi prime whose digital root is equal to $8$. Example: $$ 17 \cdot 19 = 323 $$ The digital root of ...