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%I #9 Oct 01 2013 21:35:18
%S 7,19,73,241,411379,693110401,80746825394092993,
%T 15848109838244286131940714481,
%U 12238279486576766124458805567902551228138920205718424019
%N Primes in A002533.
%C Starting with the fraction 1/1, generate the sequence of fractions A002533(i)/A002532(i) according to the rule: "add top and bottom to get the new bottom, add top and 6 times bottom to get the new top."
%C The prime numerators of these fractions are listed here, at locations i= 2, 3, 4, 5, 11, 17, 32, 53,... showing prime(4), prime(8), prime(21), prime(53), prime(34719),..
%C Is there an infinity of primes in this sequence?
%D Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
%F A002533 INTERSECT A000040.
%o (PARI) primenum(n,k,typ) = \\ k=mult,typ=1 num,2 denom. output prime num or denom.
%o { local(a,b,x,tmp,v); a=1;b=1;
%o 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","); ) );
%o print(); print(a/b+.) }
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Oct 02 2005
%E Simplified the definition, listed some A002533 indices. - _R. J. Mathar_, Sep 16 2009
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