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%I #10 Jan 04 2024 18:24:47
%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]
%t Select[NestList[(Numerator[#]+4*Denominator[#])/(Numerator[#]+Denominator[#])&,1/1,200]//Numerator,PrimeQ] (* _Harvey P. Dale_, Jan 04 2024 *)
%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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