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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Oct 02 2005
EXTENSIONS
Definition simplified by R. J. Mathar, Jun 15 2010
STATUS
approved