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A111015
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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 10 times bottom to get the new top." Also A015519(n) is prime.
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0
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11, 31, 601, 10711, 45281, 3245551, 4057691201, 87818089575031, 813086055916584907683448771376472778745411281, 16071419731004292876206308878779566599797733387541964081866111137961
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OFFSET
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1,1
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COMMENTS
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Conjecture: Starting with 1/1, there is an infinity of primes in the numerators of fractions built according to the rule - add top and bottom to get the new bottom, add top and 2k times bottom to get the new top. k=1,2..infinity.
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REFERENCES
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Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
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LINKS
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Table of n, a(n) for n=1..10.
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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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MATHEMATICA
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Select[Numerator/@NestList[(10Denominator[#]+Numerator[#])/ (Denominator[#]+ Numerator[#])&, 1/1, 200], PrimeQ] (* Harvey P. Dale, Sep 15 2011 *)
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PROG
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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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Sequence in context: A328715 A163763 A201808 * A143765 A023306 A068839
Adjacent sequences: A111012 A111013 A111014 * A111016 A111017 A111018
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Cino Hilliard, Oct 02 2005
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STATUS
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approved
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