[seqfan] All the metal mean sequence primes.

[DAN_CYN_J]

Hi seqfans, 

  

Starting with the Fibonacci sequence. 
Excluding the first two terms of each sequence. 
Because these are each sequence's two generators. 
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. 

  

I hope I found them all up too 1601 where I might have missed one. 

The last prime in the above sequence was pulled from metal mean M(40) in the third term. 
Where f(1) is the golden mean sequence. M(40) includes the Fibonacci in the 
count of sequences. 
(sqrt(((40/2)^2)+1) +20) * 40 +1 =int(1601) 


(7) of the above primes are from the Fibonacci sequence ending @ f(17) =(1597) 
Given all the metal mean sequence --->oo I believe the Fibonacci will 
have the most primes up too any prime in the above sequence. 

Also all the in-dices are prime in the metal mean sequences 
that these primes appear in. 
The same thing as in the Fibonacci sequence. 



See also A005478 

  

Dan