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# Tag Archives: sequence

## The Recamán sequence

I recently learned about a really interesting sequence of integers, called the Recamán sequence (it’s sequence A005132 in the Online Encyclopedia of Integer Sequences). It is very simple to define, but the resulting complexity shows how powerful self-reference is (for … Continue reading

Posted in arithmetic, recursion, sequences
Tagged difference, integers, Recamán, repeat, sequence
5 Comments

## Post without words #5, explained

If you stared for a while at the images in my previous post, you probably noticed some patterns, and maybe you even figured out some sort of rule or algorithm behind them. Commenter Yammatak expressed it as “You split it … Continue reading

Posted in pattern, pictures, posts without words, sequences, solutions
Tagged curve, Hilbert, Prouhet-Thue-Morse, sequence, space-filling, Thue-Morse
4 Comments

## What does “close to” mean?

Continuing from last time, consider the (normal, decimal) number with an infinite number of 3’s after the decimal point. Now, you probably know that this represents . But why? How do we define what such an infinite sequence of digits … Continue reading

Posted in convergence, number theory
Tagged absolute value, Cauchy, distance, limit, sequence
3 Comments

## Predicting Pi: solution

Now for the solution to the question in my previous post, which asked what you can learn about , given the sequence of integers . Nick Johnson commented: Well, the obvious thing one can learn given just |(10^n)r| is the … Continue reading

Posted in convergence, pattern, sequences, solutions
Tagged approximants, approximation, floor, pi, sequence
5 Comments

## Predicting Pi

Inspired by a recent post over at Foxmaths!, here’s an interesting challenge question for you to think about: Suppose I give you the sequence of integers , and so on, where denotes the greatest integer less than or equal to … Continue reading