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May 10th, 2013, 12:06 AM  #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, 05:43 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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, 05:50 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, 07:48 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, 10:26 AM  #5 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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, 06:35 PM  #6 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Conjecture on cycle length and primes : prime abc conjec
Nice!


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abc, conjecture, cycle, length, prime, primes 
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