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A111009
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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.
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0
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5, 13, 41, 1093, 797161, 21523361, 926510094425921, 1716841910146256242328924544641, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Or, A046717(n) is prime.
Is this sequence infinite?
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REFERENCES
| Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
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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 (mathar(AT)strw.leidenuniv.nl), Aug 18 2008]
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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+.) }
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CROSSREFS
| Cf. A088553. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 18 2008]
Sequence in context: A164907 A085601 A147718 * A012172 A066873 A105262
Adjacent sequences: A111006 A111007 A111008 * A111010 A111011 A111012
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Oct 02 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008
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