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

[zak seidov]

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.


--- Peter Pein <petsie at dordos.net> wrote:

> Antti Karttunen schrieb:
> > Peter Pein wrote:
> > 
> >> zak seidov schrieb:
> >>  
> >>
> >>> Dear seqfans,
> >>>
> >>> Anyone with C++ may wish to add more terms?
> >>>
> >>> Thanks, Zak
> >>>
> >>> %S A000001
> >>>
>
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
> >>>
> >>> %N A000001 a(1) =2 , a(2) = 3, a(n) = least
> prime such
> >>> that a(n-2) | (a(n)+a(n-1))
> >>> %A A000001 Zak Seidov  (zakseidov at gmail.com),
> Jan 07
> >>> 2007
> >>>
> >>>   
> >> Sorry,
> >>
> >> I do not understand, why a(3) = 5 > 3, because 2
> | (3 + 3)
> >> ??
> >>  
> >>
> > I think it's a hidden unconscious assumption we
> are all sometimes guilty
> > of. In this case: "and different from the previous
> term".
> > 
> > -- Antti
> > 
> >> Peter
> >>
> 
> But even then, (7013 + 5) / 11 = 638.
> 
> 379 is the seventh prime with mod(7013 + p, 11) = 0:
> 
> Select[Prime[Range at PrimePi[500]],Mod[7013+#,11]==0&]
> --> {5, 71, 137, 181, 269, 313, 379, 401, 467}
> 
> 
> anList[n_ /; n >= 3] :=
>   Nest[Append[#1,
>      Function[lst, Module[{a2, a1},
>         {a2, a1} = lst;
>          NestWhile[
>           #1 + a2 & ,
>           a2 - Mod[a1, a2],
>           #1 < 2 || #1 ===a1 || Mod[#1 + a1, a2] =!=
> 0 || !PrimeQ[#1] &]
>      ]][Take[#1, -2]]] & ,
>    {2, 3}, n]
> 
> lst50 = anList[50]
> -->
> {2, 3, 5, 7, 3, 11, 7, 37, 5, 439, 11, 7013, 5,
> 42073, 2, 42071, 3, 168281, 7,
>  673117, 3, 21539741, 7, 86158957, 11, 344635817, 2,
> 1723179083, 3, 892716329,
>  7, 165425191889, 29, 7278708443087, 19,
> 43672250658503, 71, 2183612532925079,
>  829, 183423452765705807, 11, 13573335504662229707,
> 7, 244320039083920134719,
>  29, 488640078167840269409, 113,
> 12704642032363847004521, 881,
>  863915658200741596306547, 1093,
> 5183493949204449577838189}
> 
> Union[Apply[Mod[#2 + #3, #1] & , Partition[lst50, 3,
> 1], {1}]]
> 
> --> {0}
> 
> 


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