A111012 Primes in A002532.

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

Offset

1,1

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

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

Links

Table of n, a(n) for n=1..10.

Formula

A002532 INTERSECT A000040.

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

Sequence in context: A028989 A113575 A173640 * A256516 A157066 A202740

Adjacent sequences: A111009 A111010 A111011 * A111013 A111014 A111015

Keyword

easy,nonn

Author

Cino Hilliard, Oct 02 2005

Extensions

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

Status

approved