Amazing function (Collatz Problem)

f(x)=3x+1xεoddpositiveinteger=x/2xεevenpositiveintegerf\left( x \right) =\quad \quad \quad 3x+1\quad \quad \forall \quad x\quad \varepsilon \quad odd\quad positive\quad integer\\ \quad \quad \quad =\quad \quad \quad x/2\quad \quad \quad \quad \forall \quad x\quad \varepsilon \quad even\quad positive\quad integer

use this function repeatedly you will always get the answer as 1( it may take a numerous steps for certain numbers ) it always ends with the series 4,2,1

let x=28

Operating this function repeatedly (Used the function for 11 times)

x=28>14>7>22>11>34>17>52>26>13>40>20>10>5>16>8>4>2>1

let x=37

Operating this function repeatedly (used the function for 71 times)

x=37>111>334>167>502>251>754>377>1132>566>283>850>425>1276>638>319>958>479>1438>719>2158

1079>3238>1619>4858>2429>7288>3644>1822>911>2734>1367>4102>2051>6154>3077>9232>4616>2308>1154>577>1732>866>433>1300>650>325>976>488>244>122>61>184>92>46>23>70>35>106>53>160>80>40>20>10>5>16>8>4>2>1

Note by Anirudha Nayak
5 years, 6 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Nice function, but there is a mistake when you put x=28x=28. When plugging in x=11x=11, you get 3434 and not 3232.

Anish Puthuraya - 5 years, 6 months ago

Log in to reply

It is an open conjecture that it "always ends with the series 4, 2, 1". It's been verified for the first few cases, but there are infinitely many more possibilities left.

Calvin Lin Staff - 5 years, 6 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...