Jump to content
BrainDen.com - Brain Teasers
  • 0

beauty and the beast


Question

consider the golden ratio.

1.618....

now, imagine multiplying this by each integer. keep the numbers it truncates to.

1

1.618*2 = 3

1.618*3 = 4

1.618*4 = 6

1.618*5 = 8

1.618*6 = 9

and so on.

its a very interesting sequence with some "nice" properties.

now here's my question. if you're allowed any irrational number;

which one goes through the most primes and fewest composites?

Link to post
Share on other sites

2 answers to this question

Recommended Posts

  • 0

Prime numbers (greater than 3) are of the form 6n+1 or 6n-1

Since approximating 6n+1 using a rational number will be difficult as n increases, lets consider only 6n-1 cases.

As we are rounding down the numbers, an expression close to but only just less than 6 that gives all the numbers of form 6n-1, will have almost a third of the numbers prime.

Therefore using 5.99999999... we would get all 6n-1 numbers and nearly 1/3 of these numbers would be prime

Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...