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A111013
Prime numbers in A084058.
1
113, 401, 1294393, 18976049, 1064876737, 59752621657, 1865194962833120965649, 183321526083153004322945764563755249, 11875185018427998198607516048921647377541318041456866528702638540422037754393
OFFSET
1,1
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?
REFERENCES
John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
LINKS
MATHEMATICA
Select[LinearRecurrence[{2, 7}, {1, 1}, 135], PrimeQ] (* Amiram Eldar, Jun 30 2024 *)
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+.) }
CROSSREFS
Cf. A084058.
Sequence in context: A142781 A323176 A365581 * A300537 A342816 A353957
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Oct 02 2005
EXTENSIONS
Definition simplified by R. J. Mathar, Jun 15 2010
STATUS
approved