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
votes
1answer
56 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.
1
vote
1answer
44 views

Function for numeric input output series

I am trying to find function which will give me output for corresponding inputs. ...
0
votes
1answer
27 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} {5!},\frac{-3}...
0
votes
2answers
421 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
60 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
72 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 ...
-3
votes
2answers
67 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
37 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 9....
0
votes
3answers
41 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 ...
-1
votes
1answer
98 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
81 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
29 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
75 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
348 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
330 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
31 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
83 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
44 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
35 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?
1
vote
1answer
75 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 ...
23
votes
2answers
352 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
76 views

what is the formula for this function?

I've been thinking about the differences in numbers so for example: $\begin{array}{ccccccc} &&&0&&&\\ &&1&&1&&\\&1&&2&&3&\\0&...
0
votes
3answers
449 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
115 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
158 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. However,...
1
vote
2answers
53 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
45 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
63 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 higher-...
0
votes
0answers
74 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
361 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 ...
1
vote
1answer
64 views

Solving a Recurrence for a Mathematical Game

The problem is: Two players take turns removing coins from a pile. There are initially $n$ coins, and on each turn, a player can remove $a_1, a_2, \dotsc, a_k$ coins. The player who cannot remove ...
1
vote
1answer
128 views

Listing elements from set-builder notation, and vice versa

I have trouble translating from a set-builder notation to a "dotted set" $$\{\ldots,v_1,v_2,v_3,\ldots\}$$ and vice-versa. Set-builder to dotted set: $$\begin{align*} A &= \{5a+ 2b : a,b \in \...
1
vote
1answer
124 views

Is there a pattern of the length between one even Fibonacci number and another?

I had seen a math problem asking for the sum of all even Fibonacci numbers up to 4 million, but I still need to know this: Is there an obvious pattern of the distance between a even Fibonacci number ...
5
votes
0answers
169 views

What Constitutes a Pattern

Mathematics is often referred to as the "study of patterns." What I'm wondering is whether there is somehow a technical way to describe a pattern. For the length of this question let's assume that we'...
1
vote
2answers
55 views

Extracting formula from a pattern(table)

I am trying to solve a problem that requires me to extract a formula from a table, and the table has the following pattern, \begin{array}{c|c|c|c|c|c|c} \text{row 6} & \text{26}& \text{27}&...
0
votes
1answer
162 views

Brain-explosion pattern of primes and the number 30? [closed]

Prime numbers. Elusive little snips. They give you a warm trail with a dead end. Here's another one of those pattern 'trails': $$30$$ Normal number? How about 'expanding' outward? $$29, 30, 31$$ Yea, ...
47
votes
4answers
4k views

Eyebrow-raising pattern of number of primes between terms of the Fibonacci number sequence?

So, $$1,1,2,3,5,8,13,21...$$ Any connection to primes?...it appears not. However, in between the Fibonacci numbers are how much primes? Let's see: 1 and 1 ZERO 1 and 2 NADA 2 and 3 ZILCH 3 and 5 ZIP ...
1
vote
0answers
83 views

Calculating a formula for variables with multiple values equaling the same total

I'm having a bit of trouble puzzling a formula for some code I'm using to develop a piece of software. I'm not very savvy with what the technical terms for all of what I'm describing are, but I'll try ...
2
votes
0answers
44 views

Trade-off among symmetries

Take a set $X \in \mathbb{R}^2$ of nonzero measure $\mu(X) \neq 0$. I am attempting to design a set that has the following symmetries (continuous or discrete) $1.$ Scale symmetry $2.$ Rotation ...
0
votes
1answer
179 views

Generate random number based on a certain pattern and able to test against the pattern

I have very little idea about random numbers and patterns, so I am not sure whether this is actually possible or not. I want to generate random numbers, that will follow a fixed pattern (perhaps this ...
0
votes
5answers
73 views

How can I find the general formula for the following real sequence

How can I find the general formula for the following real sequence $$(x_n)_{n \ge0}=(1,0,-1,0,\frac{1}{2},0,\frac{-1}{6},0,\frac{1}{24},0,\frac{-1}{120},\ldots)$$ I just know $x_0$ to $x_{10}$ so how ...
2
votes
1answer
76 views

How to show that $p(t|x,\mathbf x,\mathbf t)= \int p(t|x,\mathbf w)p(\mathbf w|\mathbf x, \mathbf t)d\mathbf w $

The following paragraph is approximately cited from Bishop's book, Pattern Recognition and Machine Learning. In curve fitting problem, we have training data $\mathbf x$ and $\mathbf t$, along ...
8
votes
2answers
152 views

Finding pattern

Just a puzzle. \begin{matrix} 2 & 9 & ? \\ 11 & 33 & 66 \\ 8 & 3 & 27 \\ \end{matrix} The options are $35$, $40$, $45$, $55$. $45$ is false. I ...
0
votes
1answer
27 views

What does this quantity measure?

Consider this list of numbers: $$\begin{bmatrix} 59 \\ 148 & 0.60 \\ 200 & 0.26 & 1 \\ 250 & 0.20 & 1.25 \\ 290 & 0.14 & 1.45 \\ 325 & 0.11 & 1.625 \\ 360 & 0....
0
votes
2answers
44 views

Generate equation from pattern

What equation describes the growth pattern of this sequence: P = 5,25,35,55,65,85,95... Heres the diferences: 5 (20) 25 (10) 35 (20) 55 (10) 65 ... I have tried the P = Ax + B but it doesn work ...
0
votes
1answer
56 views

Pattern Finding in terms of previous terms

Find the next terms of the pattern: $$ 1,4,24,192,2120,31140,566202 \dots$$ Tell the pattern expression. I have already tried Lagrange interpolation. But it is not accurate enough.
1
vote
0answers
91 views

Elusive closed form for card permutation problem

Does a closed form formula f(n) exist for the two rightmost columns? The two question marks are meant to be 0. The diagram is a summary of the numerical results from original question: Permutations ...
0
votes
2answers
238 views

How to find a formula for a non-obvious sequence of numbers?

Suppose I have an "arbitrary" sequence of numbers and as a convenience, I want some type of concise formula to be able to generate/regenerate that exact sequence. How can I do it? Can this be done ...
0
votes
1answer
53 views

Pattern finding of last few digit of a^b

The question is:Find the last two digits of 9^2013.(No calculators allowed to solve this question.) Options: (A)01 (B)29 (C)41 (D)81 (E)89 From this point,I will show my working, 9^2=81(Last Digit ...