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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. 0
5, 13, 41, 1093, 797161, 21523361, 926510094425921, 1716841910146256242328924544641, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 (list; graph; refs; listen; history; text; internal format)
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]

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: A164907 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

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Last modified August 25 15:34 EDT 2019. Contains 326324 sequences. (Running on oeis4.)