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 A111012 #20 Jun 30 2024 03:24:04
%S A111012 2,101,1998541,3366950329,803128907400221,16099934940822131461,
%T A111012 2279520764596558292681,6469963748546758449049574741,
%U A111012 10900112859698650263468714158129,707398563162966192697450635044051857198371361627935450689
%N A111012 Primes in A002532.
%C A111012 Starting with the fraction 1/1, generate the sequence of fractions A002533(i)/A002532(i) according to the rule: "add top and bottom to get the new bottom, add top and 6 times bottom to get the new top."
%C A111012 The prime denominators of these fractions are listed here, at locations i= 2, 5, 13, 19, 29, 37,.. 41, 53, 59, .... equalling prime(1), prime(26), prime(148838), ..
%C A111012 Is there an infinity of primes in this sequence?
%D A111012 John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
%H A111012 Amiram Eldar, <a href="/A111012/b111012.txt">Table of n, a(n) for n = 1..17</a>
%F A111012 A002532 INTERSECT A000040.
%t A111012 Select[LinearRecurrence[{2, 5}, {0, 1}, 150], PrimeQ] (* _Amiram Eldar_, Jun 30 2024 *)
%o A111012 (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 A111012 Cf. A000040, A002532, A002533.
%K A111012 easy,nonn
%O A111012 1,1
%A A111012 _Cino Hilliard_, Oct 02 2005
%E A111012 Simplified the definition, listed some A002532 indices - _R. J. Mathar_, Sep 16 2009