20060215, 09:04  #56  
May 2003
3·7·11 Posts 
Quote:
The mind boggles. 

20060215, 13:53  #57  
Jan 2005
Transdniestr
503 Posts 
I don't see where the confusion is coming from
Citrix asked:
Quote:
IF 2^10+500 was 10smooth, he wouldn't be interested in that because500>10 Numbers seemed to be checking for unsmooth numbers, which would be common. 

20060215, 17:17  #58 
Jun 2005
Near Beetlegeuse
2^{2}·97 Posts 
Okay, I see where you all are coming from.
You're saying a number can be a factor of itself. I was thinking about proper factors, where, depending on who you read, the factors of n either do not include 1 and n, or they do include 1 but not n. 
20060215, 17:58  #59 
Jun 2005
Near Beetlegeuse
2^{2}×97 Posts 
I've rewritten the code.
These are all the solutions for n < 30, x < 100. But I only looked at 2^nx. I'll do + x later if you want. 2^34 = 4 2^44 = 12 2^47 = 9 2^48 = 8 2^410 = 6 2^55 = 27 2^58 = 24 2^514 = 18 2^516 = 16 2^520 = 12 2^523 = 9 2^524 = 8 2^526 = 6 2^64 = 60 2^610 = 54 2^614 = 50 2^616 = 48 2^619 = 45 2^624 = 40 2^628 = 36 2^632 = 32 2^634 = 30 2^637 = 27 2^639 = 25 2^640 = 24 2^644 = 20 2^646 = 18 2^648 = 16 2^649 = 15 2^652 = 12 2^654 = 10 2^655 = 9 2^656 = 8 2^73 = 125 2^78 = 120 2^720 = 108 2^728 = 100 2^732 = 96 2^738 = 90 2^747 = 81 2^748 = 80 2^753 = 75 2^756 = 72 2^764 = 64 2^768 = 60 2^774 = 54 2^778 = 50 2^780 = 48 2^783 = 45 2^788 = 40 2^792 = 36 2^796 = 32 2^798 = 30 2^84 = 252 2^86 = 250 2^811 = 245 2^813 = 243 2^816 = 240 2^831 = 225 2^832 = 224 2^840 = 216 2^846 = 210 2^856 = 200 2^860 = 196 2^864 = 192 2^867 = 189 2^876 = 180 2^881 = 175 2^888 = 168 2^894 = 162 2^896 = 160 2^98 = 504 2^912 = 500 2^922 = 490 2^926 = 486 2^932 = 480 2^962 = 450 2^964 = 448 2^971 = 441 2^980 = 432 2^992 = 420 2^1016 = 1008 2^1024 = 1000 2^1044 = 980 2^1052 = 972 2^1064 = 960 2^1079 = 945 2^1123 = 2025 2^1132 = 2016 2^1148 = 2000 2^1188 = 1960 2^1246 = 4050 2^1264 = 4032 2^1296 = 4000 2^1392 = 8100 2^144 = 16380 2^1449 = 16335 2^158 = 32760 2^1598 = 32670 2^1616 = 65520 2^1732 = 131040 2^1795 = 130977 2^1864 = 262080 
20060215, 18:07  #60 
Jan 2005
Transdniestr
503 Posts 
For most of these x is still > n, right?
Last fiddled with by grandpascorpion on 20060215 at 18:08 
20060215, 19:58  #61 
Jun 2005
Near Beetlegeuse
604_{8} Posts 
You really are a hard man to please :)
Citrix said 2^881 was a solution, so it never occurred to me that you wanted x < n. Here are all the solutions for 2^n+x, n < 30, x < n+1. 2^4+2 = 18 2^5+4 = 36 2^7+7 = 135 2^10+5 = 1029 2^11+10 = 2058 
20060215, 20:24  #62 
Jan 2005
Transdniestr
503 Posts 
Ah, but later he revised it. Oh well, you have one where x=n but I'll let that slide. :)

20060215, 23:14  #63 
Jan 2005
Transdniestr
503 Posts 
I found that for numbers of the form 2^n+x being nsmooth where n>abs(x),
there are no positive or negative x solutions where n>15 and n <= 1000. 
20060216, 00:41  #64  
Jun 2003
1,579 Posts 
Quote:
I think there are very few such values, possibly finite number of them. Can this be proven. I will try to write a program soon to test huge values of n. You can also use a command line in PFGW to see if they factor or not. @Numbers. Yes I am very hard to please. 

20060216, 02:38  #65 
Jan 2005
Transdniestr
503 Posts 
The nice thing is that's so cheap to do. You only have to check thru n, not factorize the whole number.
But, why would you randomly test huge numbers without some insight as to what better candidates would be? 
20060216, 15:20  #66  
Jun 2003
11000101011_{2} Posts 
THis seems an interesting related problem.
Quote:
Citrix Last fiddled with by Citrix on 20060216 at 15:22 

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