A111009 Starting with the fraction 1/1, the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 4 times bottom to get the new top.

5, 13, 41, 1093, 797161, 21523361, 926510094425921, 1716841910146256242328924544641, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013

Offset

1,1

Comments

Or, A046717(n) is prime.

Is this sequence infinite?

References

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

Links

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

Formula

Given c(0)=1, b(0)=1 then for i=1, 2, .. c(i)/b(i) = (c(i-1)+4*b(i-1)) /(c(i-1) + b(i-1)).

A046717 INTERSECT A000040. [From R. J. Mathar, Aug 18 2008]

Mathematica

Select[NestList[(Numerator[#]+4*Denominator[#])/(Numerator[#]+Denominator[#])&, 1/1, 200]//Numerator, PrimeQ] (* Harvey P. Dale, Jan 04 2024 *)

Prog

(PARI) primenum(n, k, typ) = \ k=mult, typ=1 num, 2 denom. ouyput 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

Cf. A088553. [From R. J. Mathar, Aug 18 2008]

Sequence in context: A352916 A085601 A147718 * A012172 A316536 A211383

Adjacent sequences: A111006 A111007 A111008 * A111010 A111011 A111012

Keyword

easy,nonn

Author

Cino Hilliard, Oct 02 2005

Extensions

Edited by N. J. A. Sloane, Aug 23 2008

Status

approved