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%I #4 Mar 30 2012 17:22:26
%S 1,2,3,5,6,10,11,13,21,23,24,29,45,48,50,51,53,54,57,58,60,68,70,81,
%T 82,98,103,104,106,120,125,128,132,139,149,164,170,192,206,214,226,
%U 228,232,235,241,257,270,275,283,305,307,314,326,351,399,412,423,436,520
%N Denominators of the slowest decreasing sequence of unit fractions whose partial sums have a prime numerator.
%C By Dirichlet's Theorem, it is always possible to find the next term. See A076475 for the list of primes appearing in the numerator. Does this sum of unit fractions converge?
%e For example, 1/1 + 1/2 = 3/2, 1/1 + 1/2 + 1/3 = 11/6. However, 1/4 is not in the sequence because 1/1 + 1/2 + 1/3 + 1/4 = 25/12 and 25 is not prime.
%t nMax = 100; lst = {1}; numer = {1}; s = 1; i = 2; Do[While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[lst, i]; AppendTo[numer, Numerator[s]]; i++, {n, 2, nMax}]; lst
%Y Cf. A076475.
%Y Cf. A127515, A134411.
%K nonn,frac
%O 1,2
%A _T. D. Noe_, Oct 14 2002
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