My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 9th, 2014, 12:29 PM   #1
Newbie
 
Joined: Mar 2014

Posts: 1
Thanks: 0

Yet another riddle

In the image below, we start with the integer 1 marked in yellow. We will fill the rest of the table in counterclockwise manner with integers to infinity. What will be the sum of the numbers right above and below the number 2008?

It would be really appreciated if you can explain the logic behind this question as I have no idea how to even approach it...

Screen Shot 2014-03-09 at 20.16.47.png

Last edited by skipjack; March 15th, 2015 at 05:13 AM.
hermes2014 is offline  
 
March 9th, 2014, 09:23 PM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,659
Thanks: 964

Math Focus: Elementary mathematics and beyond
Re: Yet another riddle

45² - 2008 = 17 which is less than 45, so we know 2008 lies in the same row as 2025 (which is 45²). 47² - (17 + 1) = 2191.
43² - (17 - 1) = 1833. 1833 + 2191 = 4024, the required sum.

Last edited by skipjack; March 15th, 2015 at 05:11 AM.
greg1313 is offline  
March 9th, 2014, 10:05 PM   #3
Senior Member
 
Joined: Aug 2012

Posts: 1,659
Thanks: 427

Re: Yet another riddle

Quote:
Originally Posted by hermes2014
In the image below we start with the integer 1 marked in yellow. We will full the rest of the table in counterclockwise manner with integers to infinity.
Know what's really cool? If you make all the primes black and all the composites white, you get a very mysterious pattern that nobody understands.

http://en.wikipedia.org/wiki/Ulam_spiral

Maschke is offline  
March 9th, 2014, 11:54 PM   #4
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Yet another riddle

Yes that is cool!

I see lines everywhere , also looks like a zoomed out version of the universe.

Someone should color code the primes in the picture, i'm sure our friends at OEIS could come up with a few interesting 'color schemes'.

agentredlum is offline  
March 10th, 2014, 03:36 AM   #5
Math Team
 
Joined: Apr 2010

Posts: 2,778
Thanks: 361

Re: Yet another riddle

[color=#0000AA]Waflix[/color] made a nice website (as shown in this topic) to create all sorts of figures.
http://waflix.banaanvraag.nl/prime/
And Numberphile made a video on it
http://www.youtube.com/watch?v=3K-12i0jclM
Hoempa is offline  
March 10th, 2014, 06:03 AM   #6
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Yet another riddle

Quote:
Originally Posted by Maschke
nobody understands
Well... it's mostly explained by the Hardy-Littlewood conjecture F (and more generally, the BatemanHornStemmler conjecture), but admittedly we haven't proved those yet.
CRGreathouse is offline  
March 10th, 2014, 08:08 AM   #7
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Yet another riddle

Both links are nice ,thanx [color=#00FF00]Hoempa[/color] . I was thinking ... take the program that generates the Ulam Spiral on screen and offer options to it for color coding the pixels , for example , composites white , primes black ,

Option1: Twin primes red
Option2: 4n+1 non twin primes green
Option3: 4n-1 non twin primes yellow

For this particular example , if you click on all three options you get a picture in 4 colors.

Another way to color code the picture could be by assigning a color code to the factoring time of composites , sort of like a 'Ulam's Fractal'

I'm sure OEIS has many interesting ways to allocate primes to disjoint sets , and then we can color code them and put them on a Ulam Spiral and compare them,

I just mentioned 4 ratherr obvious color codings but there's got ro be many more 'exotic' ways.

BTW OEIS already has an option where we can 'listen' to any integer sequence in the database , how about an option to 'look' at any integer sequence in the database?

agentredlum is offline  
March 10th, 2014, 08:14 AM   #8
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Yet another riddle

Quote:
Originally Posted by agentredlum
BTW OEIS already has an option where we can 'listen' to any integer sequence in the database , how about an option to 'look' at any integer sequence in the database?
https://oeis.org/search?q=keyword%3Aloo ... ge=english
https://oeis.org/A229037/graph (e.g.)
CRGreathouse is offline  
March 10th, 2014, 08:27 AM   #9
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Yet another riddle

Ah , i wasn't aware of these options , when did you guys put this in?

agentredlum is offline  
March 10th, 2014, 08:50 AM   #10
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Yet another riddle

Quote:
Originally Posted by agentredlum
Ah , i wasn't aware of these options , when did you guys put this in?
The graphs (available on all sequences, click "graph") have been there since 2006. The keyword look, for nice-looking sequences, was just added this year.
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
riddle



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
new riddle Hoempa New Users 189 June 23rd, 2013 04:31 PM
Riddle rebecca Applied Math 2 November 6th, 2011 05:12 PM
help with a riddle adenthet Computer Science 1 August 29th, 2009 08:43 PM
riDDLE ! lisalotte New Users 4 January 21st, 2008 04:14 PM
help me with this riddle pls. . . hoaxchild Applied Math 24 October 30th, 2007 08:34 AM





Copyright © 2017 My Math Forum. All rights reserved.