Search: id:A111012
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%I A111012
%S A111012 2,101,1998541,3366950329,803128907400221,16099934940822131461,
%T A111012 2279520764596558292681,6469963748546758449049574741,
%U A111012 10900112859698650263468714158129
%N A111012 Primes in A002532.
%C A111012 Starting with the fraction 1/1, generate the sequence of fractions A002533(i)/
               A002532(i) according to
%C A111012 the rule: "add top and bottom to get the new bottom, add top and 6 times 
               bottom to get the new top."
%C A111012 The prime denominators of these fractions are listed here, at locations 
               i= 2, 5, 13, 19, 29, 37,..
%C A111012 41, 53, 59, .... equalling prime(1), prime(26), prime(148838), ..
%C A111012 Is there an infinity of primes in this sequence?
%D A111012 Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
%F A111012 A002532 INTERSECT A000040.
%o A111012 (PARI) primenum(n,k,typ) = \\ k=mult,typ=1 num,2 denom. output prime 
               num or denom.
%o A111012 { local(a,b,x,tmp,v); a=1;b=1;
%o A111012 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 A111012 print(); print(a/b+.) }
%Y A111012 Sequence in context: A035325 A028989 A113575 this_sequence A157066 A055693 
               A106299
%Y A111012 Adjacent sequences: A111009 A111010 A111011 this_sequence A111013 A111014 
               A111015
%K A111012 easy,nonn
%O A111012 1,1
%A A111012 Cino Hilliard (hillcino368(AT)hotmail.com), Oct 02 2005
%E A111012 Simplified the definition, listed some A002532 indices - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Sep 16 2009

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