This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111013 #19 Jun 30 2024 03:23:29
%S A111013 113,401,1294393,18976049,1064876737,59752621657,
%T A111013 1865194962833120965649,183321526083153004322945764563755249,
%U A111013 11875185018427998198607516048921647377541318041456866528702638540422037754393
%N A111013 Prime numbers in A084058.
%C A111013 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 A111013 The sequence contains the numerators r(i) which are prime numbers.
%C A111013 Is this sequence infinite?
%D A111013 John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
%H A111013 Amiram Eldar, <a href="/A111013/b111013.txt">Table of n, a(n) for n = 1..15</a>
%t A111013 Select[LinearRecurrence[{2, 7}, {1, 1}, 135], PrimeQ] (* _Amiram Eldar_, Jun 30 2024 *)
%o A111013 (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 A111013 Cf. A084058.
%K A111013 easy,nonn
%O A111013 1,1
%A A111013 _Cino Hilliard_, Oct 02 2005
%E A111013 Definition simplified by _R. J. Mathar_, Jun 15 2010