a(n-2) | (a(n)+a(n-1)): only primes

[Peter Pein]

zak seidov schrieb:
> Dear Antti, Peter, seqfrans.
> 
> I'm sorry, but initially I meant: 
> a(n-2) = the largest prime factor of  (a(n)+a(n-1)),
> but during calculations (as Mmca is very slow)
> I changed to interactive way, and after it
> I even changed the description 
> (correct or not, this isn't what I meant anyway).
>  
> So I ask C++ and Mmca gurus to check how many terms
> are OK according to this correct definition,
> and add (optionally) new terms.
> 
> After it, %N A126607 may be changed to 
> 
> %N A126607 a(1) = 2 , a(2) = 3, a(n) = a least prime
> such that a(n-2) is the largest prime factor of
> (a(n)+a(n-1)).
> 
> Thank you all responding,
> Zak
> 
> PS If time allows
> I'll explain, hopefully, the "origin" of this 
> (not arbitrarily contrived) 
> sequence.

Well this need only some minor changes in the Mma script.

a(1) ... a(50) are:
2, 3, 5, 7, 3, 11, 7, 37, 5, 439, 11, 7013, 379, 27673, 373, 54973, 977,
548753, 4229, 7678313, 10009, 230339381, 27763, 5067438619, 197297,
273641488129, 375209, 14229357007499, 5322971, 369963276872003, 60154183,
64373610115574339, 2391404069, 514988878533190643, 25988424461,
12359733058808150971, 947488779271, 370791990816755749859, 11442511248781,
19281183511028787743887, 250300153417421, 809809707212908931825833,
1974623126029513, 40490485358670823465262137, 91776817640360519,
647847765646956357803833673, 5383737683261868781,
73854645278369287106375169941, 626134100498015370463,
886255742714297344778486668829


Peter