A111012 Primes in A002532.

2, 101, 1998541, 3366950329, 803128907400221, 16099934940822131461, 2279520764596558292681, 6469963748546758449049574741, 10900112859698650263468714158129, 707398563162966192697450635044051857198371361627935450689

Offset: 1

Author

Cino Hilliard, Oct 02 2005

Keywords

• easy
• nonn

Comments

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."

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), ..

Is there an infinity of primes in this sequence?

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..17

Crossrefs

Cf. A000040, A002532, A002533.

Programs

Mathematica

Select[LinearRecurrence[{2, 5}, {0, 1}, 150], 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+.); }

Formula

A002532 INTERSECT A000040.

Extensions

Simplified the definition, listed some A002532 indices - R. J. Mathar, Sep 16 2009