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

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..15

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

Adjacent sequences: A111010 A111011 A111012 * A111014 A111015 A111016

Keyword

easy,nonn

Author

Cino Hilliard, Oct 02 2005

Extensions

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

Status

approved