
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 9th, 2013, 11:06 PM  #1 
Member Joined: Oct 2010 Posts: 72 Thanks: 3  Conjecture on cycle length and primes : prime abc conjecture Thanks for Charles at math.stackexchange convert my language to readable math language . Suppose a>9 is odd and b is the cycle length of a as defined below. Then I conjecture that if [attachment=1:2rcl19rx]c.jpg[/attachment:2rcl19rx] for some positive integer c then a is prime. Cycle length: a is an odd number > 9 and Od is the odd part function, Sloane's A000265. Let a(0) = 1 and a(n) = Od(a(n1) + a) for n > 0. If a(n) = 1 for 0 < n < N/2  1 then the cycle length is the smallest such n, otherwise it is a/2  1. For more information see A179382. Example: 11 = 5*2^1+1 11 (1,3, 7, 9, 5) 97 = 24*2^2+1 97 (1,49, 73, 85, 91, 47, 9, 53, 75, 43, 35, 33, 65, 81, 89, 93, 95, 3, 25, 61, 79, 11, 27, 31) if c = 1 that's OEIS A001122 if c = 2 that's OEIS A155072 if c = 3 that's OEIS A001134 if c = 4 that's 1217, 1249, 1553, 4049, 4273, 4481, 4993..., not in the OEIS PARI/GP code: [attachment=0:2rcl19rx]Pari_GP.jpg[/attachment:2rcl19rx] 
May 10th, 2013, 04:43 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Conjecture on cycle length and primes : prime abc conjec
That was me. I did my best to explain it and I voted to reopen the question after it had been closed initially. But I still don't have much insight into what this cycle length is and without that I'm stumbling around in the dark. 
May 10th, 2013, 04:50 AM  #3  
Member Joined: Oct 2010 Posts: 72 Thanks: 3  Re: Conjecture on cycle length and primes : prime abc conjec Quote:
That thanks!  
May 15th, 2013, 06:48 AM  #4 
Member Joined: Oct 2010 Posts: 72 Thanks: 3  Re: Conjecture on cycle length and primes : prime abc conjec
Thanks for CRG's rewrite, OEIS published a sequence generated by prime abc conjecture when c = 4 on May 15, 2013,see https://oeis.org/A225759.

May 15th, 2013, 09:26 AM  #5 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Conjecture on cycle length and primes : prime abc conjec
Congrats!

May 15th, 2013, 05:35 PM  #6 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Conjecture on cycle length and primes : prime abc conjec
Nice!


Tags 
abc, conjecture, cycle, length, prime, primes 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Mersenne Primes and Goldbach Conjecture  goodjobbro  Number Theory  2  December 1st, 2013 10:38 PM 
Conjecture about primes of a special form  Sebastian Garth  Number Theory  9  November 22nd, 2013 02:38 PM 
The proof of the Twin Primes conjecture  Al78Ex53:Fe#!D%03  Number Theory  3  September 30th, 2013 04:52 PM 
Twin primes conjecture  ibougueye  Number Theory  1  August 13th, 2012 08:24 PM 
New conjecture about primes ?  Bogauss  Number Theory  32  March 1st, 2012 06:30 AM 