Arithmetic functions | Integer sequences

Integer sequence

In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula n2 − 1 for the nth term: an explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the nth perfect number. (Wikipedia).

Integer sequence
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Introduction to Sequences (Discrete Math)

This video introduces sequences for a discrete math class. mathispower4u.com

From playlist Sequences (Discrete Math)

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What is an arithmetic sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the definition of an arithmetic sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the formula for the rule for the nth term of a arithmetic sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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Finding the rule of the sequence using multiplication and addition

👉 Learn how to write the explicit formula for the nth term of an arithmetic sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. An arithmetic sequence is a sequence in which each term of the sequence

From playlist Sequences

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What is the difference between finite and infinite sequences

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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Introduction to Sequences

This video introduces sequences. http://mathispower4u.yolasite.com/

From playlist Infinite Series

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Finding the rule for our sequence using multiplication and subtraction

👉 Learn how to write the explicit formula for the nth term of an arithmetic sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. An arithmetic sequence is a sequence in which each term of the sequence

From playlist Sequences

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How to find the rule of a arithmetic sequence given two values in the sequence

👉 Learn how to write the explicit formula for the nth term of an arithmetic sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. An arithmetic sequence is a sequence in which each term of the sequence

From playlist Sequences

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Lecture 4 - Floors and Ceilings

This is Lecture 4 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2004.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

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PotW: 5 Integers whose sum and product are less than 10 [Combinatorics]

Is this problem as easy as abc? For the written solution, check out the blog! https://centerofmathematics.blogspot.com/2019/11/potw-5-integers-whose-sum-and-product.html

From playlist Center of Math: Problems of the Week

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Graph Theory: 44. Degree Sequence of a Tree

In this video I provide a proof of a necessary and sufficient condition for a sequence of positive integers to be a degree sequence of a tree. Bits of Graph Theory by Dr. Sarada Herke. Links to the related videos: http://youtu.be/aNKO4ttWmcU - Graph Theory: 42. Degree Sequences and Graph

From playlist Graph Theory part-8

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Florian Pausinger: Part 3: Greedy energy minimization and thevan der Corput sequence

VIRTUAL LECTURE Recording during the meeting "Discrepancy Theory and Applications". Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywo

From playlist Jean-Morlet Chair - Tichy/Rivat

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Real numbers Cauchy construction

Cauchy Construction of the Real Numbers In this video, I will show you how to construct the real numbers, but in a cool way! This approach does not use Dedekind cuts or Decimal expansions, but instead Cauchy sequences. Watch this video and be amazed! Dedekind Cuts: https://youtu.be/ZWRnZ

From playlist Sequences

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Worldwide Calculus: Theorems on Sequences

Lecture on 'Theorems on Sequences' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.

From playlist Worldwide Single-Variable Calculus for AP®

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Émilie Charlier: Logic, decidability and numeration systems - Lecture 1

Abstract: The theorem of Büchi-Bruyère states that a subset of Nd is b-recognizable if and only if it is b-definable. As a corollary, the first-order theory of (N,+,Vb) is decidable (where Vb(n) is the largest power of the base b dividing n). This classical result is a powerful tool in ord

From playlist Mathematical Aspects of Computer Science

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Predicting the rules behind - Deep Symbolic Regression for Recurrent Sequences (w/ author interview)

#deeplearning #symbolic #research This video includes an interview with first author Stéphane d'Ascoli (https://sdascoli.github.io/). Deep neural networks are typically excellent at numeric regression, but using them for symbolic computation has largely been ignored so far. This paper use

From playlist Papers Explained

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Given two terms find the rule of the arithmetic sequence

👉 Learn how to write the explicit formula for the nth term of an arithmetic sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. An arithmetic sequence is a sequence in which each term of the sequence

From playlist Sequences

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1.11.4 Cantor's Theorem: Video

MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015

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