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A111015 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. 0
11, 31, 601, 10711, 45281, 3245551, 4057691201, 87818089575031, 813086055916584907683448771376472778745411281, 16071419731004292876206308878779566599797733387541964081866111137961 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

REFERENCES

Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

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)).

MATHEMATICA

Select[Numerator/@NestList[(10Denominator[#]+Numerator[#])/ (Denominator[#]+ Numerator[#])&, 1/1, 200], PrimeQ] (* Harvey P. Dale, Sep 15 2011 *)

PROG

(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+.) }

CROSSREFS

Sequence in context: A093881 A163763 A201808 * A143765 A023306 A068839

Adjacent sequences:  A111012 A111013 A111014 * A111016 A111017 A111018

KEYWORD

easy,nonn,uned

AUTHOR

Cino Hilliard, Oct 02 2005

STATUS

approved

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Last modified September 21 22:00 EDT 2019. Contains 327283 sequences. (Running on oeis4.)