cp's OEIS Frontend

A239036 A set of eleven distinct positive odd numbers the sum of whose reciprocals is 1 and whose 11th term is as large as possible.

%I A239036 #37 Mar 14 2015 01:00:42
%S A239036 3,5,7,9,11,13,23,721,979011,175878510309,20622166925499467673345
%N A239036 A set of eleven distinct positive odd numbers the sum of whose reciprocals is 1 and whose 11th term is as large as possible.
%C A239036 If k is the largest number in the set of eleven distinct positive odd numbers the sum of whose reciprocals is 1, then k <= a(11).
%C A239036 Is there any set of eleven distinct positive odd numbers the sum of whose reciprocals is 1 and having the Egyptian number greater than 20622166925675347163457?
%C A239036 This is similar to the problem discussed by Curtiss (see link), but the numbers are restricted to be odd. - _T. D. Noe_, Mar 18 2014
%H A239036 D. R. Curtiss, <a href="http://www.jstor.org/stable/2299023?origin=crossref">On Kellogg's Diophantine problem</a>, Amer. Math. Monthly 29 (1922), pp. 380-387.
%H A239036 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A239036 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/13 + 1/23 + 1/721 + 1/979011 + 1/175878510309 + 1/20622166925499467673345 = 1.
%o A239036 (PARI) f=0; n=3; s=11; if(s<11, break); for(t=1, s-3, print1(n, ", "); f=f+1/n; until(1>f+1/n, n=n+2)); until(numerator(1-f-1/n)==2, n=n+2); print1(n, ", "); f=f+1/n; g=2*floor((numerator(f)+1)/4)+1; until(numerator(1-f-1/g)==1, g=g+2); print1(g, ", "); f=f+1/g; print1(denominator(1-f));
%Y A239036 Cf. A238795, A201646.
%K A239036 nonn,fini,full,nice
%O A239036 1,1
%A A239036 _Arkadiusz Wesolowski_, Mar 09 2014