A111013 - OEIS

%I #19 Jun 30 2024 03:23:29

%S 113,401,1294393,18976049,1064876737,59752621657,

%T 1865194962833120965649,183321526083153004322945764563755249,

%U 11875185018427998198607516048921647377541318041456866528702638540422037754393

%N Prime numbers in A084058.

%C 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)).

%C The sequence contains the numerators r(i) which are prime numbers.

%C Is this sequence infinite?

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

%H Amiram Eldar, <a href="/A111013/b111013.txt">Table of n, a(n) for n = 1..15</a>

%t Select[LinearRecurrence[{2, 7}, {1, 1}, 135], PrimeQ] (* _Amiram Eldar_, Jun 30 2024 *)

%o (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+.) }

%Y Cf. A084058.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Oct 02 2005

%E Definition simplified by _R. J. Mathar_, Jun 15 2010