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Search: id:A111012
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| 2, 101, 1998541, 3366950329, 803128907400221, 16099934940822131461, 2279520764596558292681, 6469963748546758449049574741, 10900112859698650263468714158129
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OFFSET
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1,1
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COMMENT
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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."
The prime denominators of these fractions are listed here, at locations i= 2, 5, 13, 19, 29, 37,..
41, 53, 59, .... equalling prime(1), prime(26), prime(148838), ..
Is there an infinity of primes in this sequence?
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REFERENCES
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Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
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FORMULA
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A002532 INTERSECT A000040.
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PROGRAM
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(PARI) primenum(n, k, typ) = \\ k=mult, typ=1 num, 2 denom. output 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+.) }
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CROSSREFS
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Sequence in context: A035325 A028989 A113575 this_sequence A157066 A055693 A106299
Adjacent sequences: A111009 A111010 A111011 this_sequence A111013 A111014 A111015
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Oct 02 2005
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EXTENSIONS
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Simplified the definition, listed some A002532 indices - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 16 2009
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