20081203, 20:26  #1 
May 2004
New York City
5×7×11^{2} Posts 
A Prime Sequence
Call a prime p "dnice" if there is another prime of the form ap +/ b,
with 1 <= a,b <= d. What are the smallest primes that are NOT dnice, for d = 1,2,3,4,5 (etc)? 
20081204, 19:46  #2 
Jan 2005
Transdniestr
767_{8} Posts 
Isn't 2 the first 1bad number?

20081204, 19:49  #3 
Aug 2006
3×1,993 Posts 
1 5
2 47 3 389 4 449 5 26627 6 47681 7 237343 8 1108337 9 2875111 10 9189181 11 12180187 12 208564813 Last fiddled with by CRGreathouse on 20081204 at 19:50 
20081204, 22:28  #4 
Jan 2005
Transdniestr
503 Posts 

20081205, 04:01  #5 
Aug 2006
5979_{10} Posts 
The original question was about primes with this property, so 226936710 isn't the 13th solution. If we allowed composites then the 5th solution is 11850, not 26627 (and so on).
Last fiddled with by CRGreathouse on 20081205 at 04:26 
20081205, 05:46  #6 
Jan 2005
Transdniestr
503 Posts 
Ah, right again. Back to the drawing board ...

20081205, 13:11  #7 
Aug 2006
13533_{8} Posts 
13 1746334757
It happens, don't worry about it. Maybe you can calculate this variant sequence? It seems to be at least as interesting as the original. Since you came up with it I'll let you have the first real whack at it. It should start like: 1 5 2 47 3 389 4 449 5 11850 (but check that, don't trust me!) 
20081205, 15:32  #8 
Jan 2005
Transdniestr
503 Posts 
13bad : 1746334757
14bad : 3170297129 (minimal primes this time) 
20081206, 00:12  #9 
Aug 2006
3×1,993 Posts 
You beat me to 14! (Your result matches mine: my computer finished it, but I didn't see the result until after your post.) Good for you. I'm working on 15 now; since I only just started I imagine you'll win there, too.
Last fiddled with by CRGreathouse on 20081206 at 00:13 
20081206, 06:05  #10 
Jan 2005
Transdniestr
767_{8} Posts 
By the way, I checked through 4 billion. No results for 15. I'm done for now anyways :)

20081206, 15:38  #11 
Aug 2006
3·1,993 Posts 

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