%I A076476
%S A076476 1,1,1,3,1,1,1,3,4,1,5,1,1,3,1,9,1,7,4,3,1,5,1,23,9,3,10,13,13,29,7,19,
%T A076476 5,21,2,17,2,3,7,7,5,5,6,7,1,43,3,59,27,17,4,5,9,7,1,9,2,9,7,29,8,9,4,
%U A076476 25,3,119,2,27,4,29,4,37,5,3,2,5,9,7,10,49,1,35,12,11,6,1,22,1,13,11,4
%N A076476 Fractions a(n)/n are such that gcd(a(n),n)=1, a(n) > 0 and a(n) is as 
               small as possible so that the partial sums of the fractions have 
               prime numerator. Let a(1)=1.
%C A076476 By Dirichlet's Theorem, it is always possible to find the next term. 
               See A076477 for the list of primes appearing in the numerator. The 
               denominators of these sums are the same as for harmonic numbers, 
               A002805. The sum of the fractions diverges. Is there an upper bound 
               for a(n)/n?
%e A076476 a(4) = 3 because 1/4 yields 1/1 + 1/2 + 1/3 + 1/4 = 25/12, but 3/4 yields 
               1/1 + 1/2 + 1/3 + 3/4 = 31/12.
%t A076476 nMax = 100; lst = {1}; numer = {1}; s = 1; Do[k = 1; While[GCD[k, n] 
               > 1 || ! PrimeQ[Numerator[s + k/n]], k++ ]; s = s + k/n; AppendTo[lst, 
               k]; AppendTo[numer, Numerator[s]]; k++, {n, 2, nMax}]; lst
%Y A076476 Cf. A076477.
%Y A076476 Sequence in context: A166030 A132890 A069290 this_sequence A016733 A060234 
               A131270
%Y A076476 Adjacent sequences: A076473 A076474 A076475 this_sequence A076477 A076478 
               A076479
%K A076476 nonn,frac
%O A076476 1,4
%A A076476 T. D. Noe (noe(AT)sspectra.com), Oct 14 2002