Tag Archives: powers

The curious powers of 1 + sqrt 2: recurrences

Posted on July 6, 2017 by

In my previous post, we found an answer to the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? However, the solution depended on having the clever idea to add . … Continue reading →

Posted in number theory, puzzles | Tagged , , , , , | 8 Comments

The curious powers of 1 + sqrt 2: a clever solution

Posted on June 21, 2017 by

Recall that we are trying to answer the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? In my previous post, we computed for some small and conjectured that the answer … Continue reading →

Posted in number theory, puzzles | Tagged , , , , , | 2 Comments

The curious powers of 1 + sqrt 2: conjecture

Posted on June 17, 2017 by

In my previous post I related the following puzzle from Colin Wright: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Let’s play around with this a bit and see if we … Continue reading →

Posted in number theory, puzzles | Tagged , , , , , | 3 Comments

The curious powers of 1 + sqrt 2

Posted on June 6, 2017 by

Recently on mathstodon.xyz, Colin Wright posted the following puzzle: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Of course, it’s simple enough to use a computer to find the answer; any … Continue reading →

Posted in challenges, number theory, puzzles | Tagged , , , | 15 Comments

Differences of powers of consecutive integers, part II

Posted on February 16, 2012 by

If you spent some time playing around with the procedure from Differences of powers of consecutive integers (namely, raise consecutive integers to the th power, and repeatedly take pairwise differences until reaching a single number) you probably noticed the curious … Continue reading →

Posted in arithmetic, iteration, pascal's triangle | Tagged , , , , | 3 Comments

Differences of powers of consecutive integers

Posted on January 29, 2012 by

Patrick Vennebush of Math Jokes 4 Mathy Folks recently wrote about the following procedure that yields surprising results. Choose some positive integer . Now, starting with consecutive integers, raise each integer to the th power. Then take pairwise differences by … Continue reading →

Posted in arithmetic, pattern | Tagged , , , , | 16 Comments