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Search: id:A111008
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| A111008 |
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Starting a priori 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 twice bottom to get the new top." Also A001333(n) is prime. |
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+0
1
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| 3, 7, 17, 41, 239, 577, 665857, 9369319, 63018038201, 489133282872437279, 19175002942688032928599, 123426017006182806728593424683999798008235734137469123231828679
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Is there an infinity of primes in this sequence?
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REFERENCES
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Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
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FORMULA
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Given a(0)=1, b(0)=1 then for i=1, 2, .. a(i)/b(i) = (a(i-1)+2*b(i-1)) /(a(i-1) + b(i-1)).
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PROGRAM
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(PARI) primenum(n, k, typ) = \yp = 1 num, 2 denom. print only 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
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Sequence in context: A131721 A058351 A086395 this_sequence A020730 A003440 A102071
Adjacent sequences: A111005 A111006 A111007 this_sequence A111009 A111010 A111011
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 02 2005
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