Base-dependent integer sequences
Aronson's sequence is an integer sequence defined by the English sentence "T is the first, fourth, eleventh, sixteenth, ... letter in this sentence." Spaces and punctuation are ignored. The first few numbers in the sequence are: 1, 4, 11, 16, 24, 29, 33, 35, 39, 45, 47, 51, 56, 58, 62, 64, 69, 73, 78, 80, 84, 89, 94, 99, 104, 111, 116, 122, 126, 131, 136, 142, 147, 158, 164, 169, ... (sequence in the OEIS). In Douglas Hofstadter's book Metamagical Themas, the sequence is credited to Jeffrey Aronson of Oxford, England. The sequence is infinite—and this statement requires some proof. The proof depends on the observation that the English names of all ordinal numbers, except those that end in 2, must contain at least one "t". Aronson's sequence is closely related to autograms. There are many generalizations of Aronson's sequence and research into the topic is ongoing. write that Aronson's sequence is "a classic example of a self-referential sequence." However, they criticize it for being ambiguously defined due to the variation in naming of numbers over one hundred in different dialects of English. In its place, they offer several other self-referential sequences whose definitions rely only on mathematics rather than on the English language. (Wikipedia).
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
Finding the first four terms of a sequence given a factorial
👉 Learn how to find the first five terms of a sequence. Given an explicit formula for a sequence, we can find the nth term of the sequence by plugging the term number of the sequence for n in the given formula. When n = 1, 2, . . ., 5 are plugged into the explicit formula, we obtain the fi
From playlist Sequences
This video introduces sequences. http://mathispower4u.yolasite.com/
From playlist Infinite Series
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
How to find the first four terms of a sequence
👉 Learn how to find the first five terms of a sequence. Given an explicit formula for a sequence, we can find the nth term of the sequence by plugging the term number of the sequence for n in the given formula. When n = 1, 2, . . ., 5 are plugged into the explicit formula, we obtain the fi
From playlist Sequences
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
Write the first five terms of a sequence with factorials
👉 Learn how to find the first five terms of a sequence. Given an explicit formula for a sequence, we can find the nth term of the sequence by plugging the term number of the sequence for n in the given formula. When n = 1, 2, . . ., 5 are plugged into the explicit formula, we obtain the fi
From playlist Sequences
The Mathematics of Consciousness
Go to http://ow.ly/4nK830rrtFY to check out The Great Courses Plus and start your free trial! Addendum to what I say at 5 mins 18 seconds: Tegmark's claim about the decoherence time has been disputed by Hameroff et al https://journals.aps.org/pre/abstract/10.1103/PhysRevE.65.061901 Pleas
From playlist Science Explainers
Finding the first four terms of a sequence with a rational rule
👉 Learn how to find the first five terms of a sequence. Given an explicit formula for a sequence, we can find the nth term of the sequence by plugging the term number of the sequence for n in the given formula. When n = 1, 2, . . ., 5 are plugged into the explicit formula, we obtain the fi
From playlist Sequences
A nearly optimal lower bound on the approximate degree of AC00- Mark Bun
Computer Science/Discrete Mathematics Seminar I Topic: A nearly optimal lower bound on the approximate degree of AC00 Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker: Mark Bun Affiliation: Princeton University Date: October 23, 2017 For more videos, pleas
From playlist Mathematics
Lecture 2, Unintended Consequences: Antonio del Pollaiuolo's Hercules and Deianira (c. 1475-80)
The Gallery's best known Renaissance painting shows Hercules about to shoot a centaur who is abducting his bride. Everybody admires the vigorous action and vast landscape. What about the subject? In the myth, she is rescued, but the shooting eventually leads to a horrible death for Hercule
From playlist Let This Be a Lesson
Given a sequence formula find the first four terms with alternating signs
👉 Learn how to find the first five terms of a sequence. Given an explicit formula for a sequence, we can find the nth term of the sequence by plugging the term number of the sequence for n in the given formula. When n = 1, 2, . . ., 5 are plugged into the explicit formula, we obtain the fi
From playlist Sequences
RubyConf2019 - Kill All Mutants! (Intro to Mutation Testing) by Dave Aronson
RubyConf2019 - Kill All Mutants! (Intro to Mutation Testing) by Dave Aronson How good are your tests? Would they still pass if the tested code was changed much? If so, you may have a problem! Mutation testing helps reveal these cases. It runs your unit tests, using many slightly altered
From playlist RubyConf 2019
Abstract: This talk describes the REDCap service at Indiana university. What is REDCap? Who uses it? And who supports it? REDCap is used by over three thousand users across several IU campuses for research data collection and for collecting and managing data in internal operations and pr
From playlist UITS Research Technologies Services
From the mediaX Conference "New Approaches to Audience Segmentation": Maurits Kaptein explores how different online persuasion strategies influence different people. Lou Aronson discusses his company’s approach to segmentation based online conversations. Joris Janssen creates tools that pr
From playlist New Approaches to Audience Segmentation Conference
Svetlana ROUDENKO - Going beyond the threshold...
Svetlana ROUDENKO - Going beyond the threshold: blow-up and scattering in the focusing NLS equation
From playlist Trimestre "Ondes Non linéaires" - Summer school
Julien Berestycki: Vanishing corrections for the position of an FKPP front
Abstract: The celebrated Fisher-Kolmogorov-Petrovsky-Piscounof equation (FKPP) in one dimension for h:ℝ×ℝ+→ℝ is: ∂th=∂2xh+h−h2,h(x,0)=h0(x). This equation is a natural description of a reaction-diffusion model (Fisher 1937, Kolmogorov et al. 1937, Aronson 1978). It is also related to bra
From playlist Probability and Statistics
9. Evolution, Emotion, and Reason: Love (Guest Lecture by
Introduction to Psychology (PSYC 110) Guest lecturer Peter Salovey, Professor of Psychology and Dean of Yale College, introduces students to the dominant psychological theories of love and attraction. Specific topics include the different types of love, the circumstances that predict attr
From playlist Introduction to Psychology with Paul Bloom
Learning to determine the first five terms of a sequence
👉 Learn how to find the first five terms of a sequence. Given an explicit formula for a sequence, we can find the nth term of the sequence by plugging the term number of the sequence for n in the given formula. When n = 1, 2, . . ., 5 are plugged into the explicit formula, we obtain the fi
From playlist Sequences
Sébastien Gouëzel: Growth of normalizing sequences in limit theorems
Abstract: Assume that a renormalized Birkhoff sum Snf/Bn converges in distribution to a nontrivial limit. What can one say about the sequence Bn? Most natural statements in the literature involve sequences Bn of the form Bn=nαL(n), where L is slowly varying. We will discuss the possible g
From playlist Probability and Statistics