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A111013
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Prime numbers in A084058.
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1
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113, 401, 1294393, 18976049, 1064876737, 59752621657, 1865194962833120965649, 183321526083153004322945764563755249, 11875185018427998198607516048921647377541318041456866528702638540422037754393
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OFFSET
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1,1
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COMMENTS
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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
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John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
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LINKS
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MATHEMATICA
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Select[LinearRecurrence[{2, 7}, {1, 1}, 135], PrimeQ] (* Amiram Eldar, Jun 30 2024 *)
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PROG
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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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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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