[seqfan] Re: All the metal mean sequence primes.

[Hans Havermann]

Dan has explained to me that he meant the sequences:

2, 3, 5, ..
5, 12, 29, ..
10, 33, 109, ..
17, 72, 305, ..
etc.

a(n) = m*a(n-1) + a(n-2), where a(1) = 1, a(2) = positive integer m, and n>2.

I confirmed his prime collection and added a few more terms.


I had written:

> On Jul 19, 2013, at 10:35 PM, DAN_CYN_J <dan_cyn_j at comcast.net> wrote:
> 
>> Where the first term generator = (1) for each sequence. 
>> Then the second term generator integer = (1,2,3,4,5,6,7...in order for each sequence.) 
>> 
>> All primes that appear in these sequence's after the second term 
>> up to 1601 are listed below. 
>> 
>> 2,3,5,13,17,29,37,89,101,109,197,233,257,401,577,677,701,1297,1597,1601--->oo. 
> 
> 
> It isn't at all clear to me what you are enumerating here but my impression is that you are combining all primes found in:
> 
> 2, 3, 5, ..
> 3, 5, 8, ..
> 4, 7, 11, ..
> 5, 9, 14, ..
> etc.
> 
> But that can't be right because *all* primes appear.