A111013 Prime numbers in A084058.

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

Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.

Links

Table of n, a(n) for n=1..9.

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

Sequence in context: A142781 A323176 A365581 * A300537 A342816 A353957

Adjacent sequences: A111010 A111011 A111012 * A111014 A111015 A111016

Keyword

easy,nonn

Author

Cino Hilliard, Oct 02 2005

Extensions

Definition simplified - R. J. Mathar, Jun 15 2010

Status

approved