A Collatz anomaly (3n+a)
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From: Danny73 on 7 Jul 2010 16:01 Where a = [41,43,61,107,113,257,739...] The two restrictions on (a) is-- (a) can't = (n) and (a) can't be a multiple of (n) Then 3n+a will always loop 4,2,1,4,2,1... with the above list of primes for any (n) other than the two restrictions on (a). Can the next prime on this list be found through some algorithm without testing? Also, do all these integers have to be prime? Dan
From: Mensanator on 8 Jul 2010 01:01 On Jul 7, 3:01 pm, Danny73 <fasttrac...(a)att.net> wrote: > Where a = [41,43,61,107,113,257,739...] > > The two restrictions on (a) is-- > (a) can't = (n) and > (a) can't be a multiple of (n) > > Then 3n+a will always loop 4,2,1,4,2,1... So? with > the above list of primes for any (n) other than > the two restrictions on (a). What does that have to do with the price of tea in China? Are you claiming there are numbers thay DON'T loop on 4,4,1? > > Can the next prime on this list be found through > some algorithm without testing? > > Also, do all these integers have to be prime? Do you not ungerstand the probem or are you just having problems rxpressing yourself? > > Dan
From: Danny73 on 8 Jul 2010 12:07 On Jul 8, 1:01 am, Mensanator <mensana...(a)aol.com> wrote: > On Jul 7, 3:01 pm, Danny73 <fasttrac...(a)att.net> wrote: > > > Where a = [41,43,61,107,113,257,739...] > > > The two restrictions on (a) is-- > > (a) can't = (n) and > > (a) can't be a multiple of (n) > > > Then 3n+a will always loop 4,2,1,4,2,1... > > So? > > with > > > the above list of primes for any (n) other than > > the two restrictions on (a). > > What does that have to do with the price of tea in China? > > Are you claiming there are numbers thay DON'T loop on 4,4,1? > > > > > Can the next prime on this list be found through > > some algorithm without testing? > > > Also, do all these integers have to be prime? > > Do you not ungerstand the probem or are you just having problems > rxpressing yourself? > > > > > > > Dan- Hide quoted text - > > - Show quoted text - I understand the problem! I am just asking do these special integers have to be prime? Also how can the next integer be found without trial and error? I just find this problem tied to 3n+1\3n+a interesting. BTW what is the next integer (prime) (a) that follows 739? Dan
From: Mensanator on 8 Jul 2010 21:51 On Jul 8, 11:07 am, Danny73 <fasttrac...(a)att.net> wrote: > On Jul 8, 1:01 am, Mensanator <mensana...(a)aol.com> wrote: > > > > > > > On Jul 7, 3:01 pm, Danny73 <fasttrac...(a)att.net> wrote: > > > > Where a = [41,43,61,107,113,257,739...] > > > > The two restrictions on (a) is-- > > > (a) can't = (n) and > > > (a) can't be a multiple of (n) > > > > Then 3n+a will always loop 4,2,1,4,2,1... > > > So? > > > with > > > > the above list of primes for any (n) other than > > > the two restrictions on (a). > > > What does that have to do with the price of tea in China? > > > Are you claiming there are numbers thay DON'T loop on 4,4,1? > > > > Can the next prime on this list be found through > > > some algorithm without testing? > > > > Also, do all these integers have to be prime? > > > Do you not ungerstand the probem or are you just having problems > > rxpressing yourself? > > > > Dan- Hide quoted text - > > > - Show quoted text - > > I understand the problem! OK, but the next question does not seem to follow from such understanding. > I am just asking do these special integers have to be prime? In order For what? To lead to the anomoly of having the sequence end in the loop 4,2,1? First of all, it's not an anomoly that ANY sequence ends tgat way since ALL of them do. Furthermore, what do ypu think the significance of the numbers being prime ia. Or for that matter, multiples of n? None of these criteria will have any bearing whatsoever on whether or nt the sequence ends in 4,2,1. Perhaps ther is some interestin gyrations that occur when said criteria are met, but you didn't ask that. You haven't even explained what the "anonoly" was. Cdrtin questions actuall DO have reasons why certain properties exist, for eample, why Mersenne numbers typically hve longer sequences than random numbers of similar size (even though all end in 4,2,1.) > Also how can the next integer be found without trial and error? > I just find this problem tied to 3n+1\3n+a interesting. > BTW what is the next integer (prime) (a) that follows 739? > > Dan
From: Danny73 on 8 Jul 2010 23:46
On Jul 8, 9:51 pm, Mensanator <mensana...(a)aol.com> wrote: > On Jul 8, 11:07 am, Danny73 <fasttrac...(a)att.net> wrote: > > > > > > > On Jul 8, 1:01 am, Mensanator <mensana...(a)aol.com> wrote: > > > > On Jul 7, 3:01 pm, Danny73 <fasttrac...(a)att.net> wrote: > > > > > Where a = [41,43,61,107,113,257,739...] > > > > > The two restrictions on (a) is-- > > > > (a) can't = (n) and > > > > (a) can't be a multiple of (n) > > > > > Then 3n+a will always loop 4,2,1,4,2,1... > > > > So? > > > > with > > > > > the above list of primes for any (n) other than > > > > the two restrictions on (a). > > > > What does that have to do with the price of tea in China? > > > > Are you claiming there are numbers thay DON'T loop on 4,4,1? > > > > > Can the next prime on this list be found through > > > > some algorithm without testing? > > > > > Also, do all these integers have to be prime? > > > > Do you not ungerstand the probem or are you just having problems > > > rxpressing yourself? > > > > > Dan- Hide quoted text - > > > > - Show quoted text - > > > I understand the problem! > > OK, but the next question does not seem to follow from > such understanding. > > > I am just asking do these special integers have to be prime? > > In order For what? To lead to the anomoly of having the > sequence end in the loop 4,2,1? Yes in this special case it is an anomoly because only these few primes (a) when added to 3n + (a) will loop 4,2,1 FOR ALL (n) except if a= n or (a) is a multiple of n. I am using (a) variable here because I am not sure if all in this list will be prime. At least the first few that I found are all prime but that does not mean that as this list continues they will all be prime. This list will probably --->oo but have no proof of that either. The latest find is 821 and 1307. Both prime. Would'nt it be something if only primes would work. Find one that is not prime where the restrictions on (a) relating too (n) is met and I will close my questioning. Is that fair enough? > First of all, it's not an anomoly that ANY sequence ends tgat way > since ALL of them do. > > Furthermore, what do ypu think the significance of the numbers being > prime > ia. Or for that matter, multiples of n? None of these criteria > will have any bearing whatsoever on whether or nt the sequence ends in > 4,2,1. > > Perhaps ther is some interestin gyrations that > occur when said criteria are met, but you didn't ask that. Like I said above, meet the restrictions on (a) relation to (n) and find a non prime in my list. > > You haven't even explained what the "anonoly" was. > > Cdrtin questions actuall DO have reasons why certain properties exist, > for eample, > why Mersenne numbers typically hve longer sequences than random > numbers of similar size (even though > all end in 4,2,1.) > > > > > Also how can the next integer be found without trial and error? > > I just find this problem tied to 3n+1\3n+a interesting. > > BTW what is the next integer (prime) (a) that follows 739? > > > Dan- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - Thanks for the input. |