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 A110881 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 twice the old bottom to get the new top. 0
 1, 2, 4, 28, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS k is the multiple 4 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, 3/2 2, 7/5 4, 41/29 28, 63018038201/44560482149 58, 19175002942688032928599/13558774610046711780701 REFERENCES Prime Obsession, John Derbyshire, Joseph Henry Press, 2004, p. 16. LINKS Table of n, a(n) for n=1..5. 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)). EXAMPLE For k=2, n = 1, we start with fraction 1/1. The new bottom is old top + old bottom = 1+1 = 2. Then we add 1 (old top) + 2*1 (old bottom) to get 3, the new top. So our first fraction is 3/2. Since these are both prime, n=1 is the first entry. Continuing with this fraction 3/2, we repeat the rule. The new bottom is 3+2 = 5. Then we add 3 + 2*2 to get 7, the new top. So our second fraction is 7/5. Since both numerator and denominator are prime, n=2 is the second entry. PROG (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+.) } CROSSREFS Sequence in context: A323447 A227303 A066228 * A156449 A259375 A192374 Adjacent sequences: A110878 A110879 A110880 * A110882 A110883 A110884 KEYWORD more,nonn AUTHOR Cino Hilliard, Oct 02 2005, Jul 05 2007 STATUS approved

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Last modified September 24 22:14 EDT 2023. Contains 365582 sequences. (Running on oeis4.)