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A239036
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A set of eleven distinct positive odd numbers the sum of whose reciprocals is 1 and whose 11th term is as large as possible.
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3
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3, 5, 7, 9, 11, 13, 23, 721, 979011, 175878510309, 20622166925499467673345
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OFFSET
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1,1
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COMMENTS
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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).
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?
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
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LINKS
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EXAMPLE
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1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/13 + 1/23 + 1/721 + 1/979011 + 1/175878510309 + 1/20622166925499467673345 = 1.
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PROG
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(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));
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CROSSREFS
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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STATUS
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approved
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