A111013 Prime numbers in A084058.

113, 401, 1294393, 18976049, 1064876737, 59752621657, 1865194962833120965649, 183321526083153004322945764563755249, 11875185018427998198607516048921647377541318041456866528702638540422037754393

Offset: 1

Author

Cino Hilliard, Oct 02 2005

Keywords

• easy
• nonn

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

Crossrefs

Cf. A084058.

Programs

Mathematica

Select[LinearRecurrence[{2, 7}, {1, 1}, 135], PrimeQ] (* Amiram Eldar, Jun 30 2024 *)

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+.) }

Extensions

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