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 A111009 Starting with the fraction 1/1, the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 4 times bottom to get the new top. 0

%I

%S 5,13,41,1093,797161,21523361,926510094425921,

%T 1716841910146256242328924544641,3754733257489862401973357979128773,

%U 6957596529882152968992225251835887181478451547013

%N Starting with the fraction 1/1, the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 4 times bottom to get the new top.

%C Or, A046717(n) is prime.

%C Is this sequence infinite?

%D Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.

%F Given c(0)=1, b(0)=1 then for i=1, 2, .. c(i)/b(i) = (c(i-1)+4*b(i-1)) /(c(i-1) + b(i-1)).

%F A046717 INTERSECT A000040. [From _R. J. Mathar_, Aug 18 2008]

%o (PARI) primenum(n,k,typ) = \ k=mult,typ=1 num,2 denom. ouyput prime num or denom. { local(a,b,x,tmp,v); a=1;b=1; for(x=1,n, tmp=b; b=a+b; a=k*tmp+a; if(typ==1,v=a,v=b); if(isprime(v),print1(v","); ) ); print(); print(a/b+.) }

%Y Cf. A088553. [From _R. J. Mathar_, Aug 18 2008]

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Oct 02 2005

%E Edited by _N. J. A. Sloane_, Aug 23 2008

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)