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 20140309 at 20.16.47.png Last edited by skipjack; March 15th, 2015 at 05:13 AM. 
March 9th, 2014, 09:23 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,881 Thanks: 1088 Math Focus: Elementary mathematics and beyond  Re: Yet another riddle
45Â²  2008 = 17 which is less than 45, so we know 2008 lies in the same row as 2025 (which is 45Â²). 47Â²  (17 + 1) = 2191. 43Â²  (17  1) = 1833. 1833 + 2191 = 4024, the required sum. Last edited by skipjack; March 15th, 2015 at 05:11 AM. 
March 9th, 2014, 10:05 PM  #3  
Senior Member Joined: Aug 2012 Posts: 2,081 Thanks: 595  Re: Yet another riddle Quote:
http://en.wikipedia.org/wiki/Ulam_spiral  
March 9th, 2014, 11:54 PM  #4 
Math Team 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'. 
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=3K12i0jclM 
March 10th, 2014, 06:03 AM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Yet another riddle Quote:
 
March 10th, 2014, 08:08 AM  #7 
Math Team 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: 4n1 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? 
March 10th, 2014, 08:14 AM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Yet another riddle Quote:
https://oeis.org/A229037/graph (e.g.)  
March 10th, 2014, 08:27 AM  #9 
Math Team 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? 
March 10th, 2014, 08:50 AM  #10  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Yet another riddle Quote:
 

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