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Search: id:A111016
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| A111016 |
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Starting with the fraction 1/1, prime denominators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 10 times bottom to get the new top. |
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+0
1
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| 2, 13, 3457, 17797573, 105563930438375514795375041782813, 548910881501677043216804568782519749
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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John Derbyshire, Prime Obsession, 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) = \ k=mult, typ=1 num, 2 denom. output 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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Also A015519(a(n)) is prime.
Sequence in context: A103641 A110820 A139519 this_sequence A118912 A135970 A027738
Adjacent sequences: A111013 A111014 A111015 this_sequence A111017 A111018 A111019
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 02 2005
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EXTENSIONS
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Edited by njas at the suggestion of Andrew Plewe, May 16 2007
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