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Search: id:A110908
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| A110908 |
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Starting a priori with the fraction 1/1, list n when the numerator and denominator are both prime for fractions built according to the rule: Add old top and old bottom to get the new bottom, add old top and 6 times the old bottom to get the new top. |
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1
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OFFSET
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1,2
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COMMENT
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k is the multiple 6 in the PARI code. The sequence of fractions found with the property that both numerator and denominator are prime is as follows.
n, num/denom
1, 7/2
4, 241/101
52, 15848109838244286131940714481/6469963748546758449049574741
106, 1732765524527243824670663837908764472971413888795440694899/7073985631629662697450635044051857198371361627935450689
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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)+6*b(i-1))/(a(i-1)+b(i-1)).
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EXAMPLE
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The first four fractions according to the rule are
n,
1,7/2
2,19/9
3,73/28
4,241/101
n=2,3 did not make the list because 9 and 28 are not prime.
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PROGRAM
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(PARI) primenumdenom(n, k) = { local(a, b, x, tmp, v); a=1; b=1; for(x=1, n, tmp=b; b=a+b; a=k*tmp+a; if(tmp=1, v=a, v=b); if(ispseudoprime(a)&ispseudoprime(b), print1(x", "); ) ); print(); print(a/b+.) }
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CROSSREFS
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Sequence in context: A048995 A000516 A000854 this_sequence A101354 A071953 A144339
Adjacent sequences: A110905 A110906 A110907 this_sequence A110909 A110910 A110911
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KEYWORD
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more,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 02 2005, Jul 05 2007
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