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A111013
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Prime numbers in A084058.
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0
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113, 401, 1294393, 18976049, 1064876737, 59752621657, 1865194962833120965649, 183321526083153004322945764563755249, 11875185018427998198607516048921647377541318041456866528702638540422037754393
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Construct a sequence of fractions r(i)/q(i) from r(0)=q(0)=1 and
recursively r(i)/q(i) = (r(i-1)+2*q(i-1)) /(r(i-1) + q(i-1)).
The sequence contains the numerators r(i) which are prime numbers.
Is this sequence infinite?
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REFERENCES
| Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
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PROG
| (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
| Sequence in context: A033249 A101217 A142781 * A142850 A203722 A118506
Adjacent sequences: A111010 A111011 A111012 * A111014 A111015 A111016
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Oct 02 2005
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EXTENSIONS
| Definition simplified - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2010
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