

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.


3



3, 5, 7, 9, 11, 13, 23, 721, 979011, 175878510309, 20622166925499467673345
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..11.
D. R. Curtiss, On Kellogg's Diophantine problem, Amer. Math. Monthly 29 (1922), pp. 380387.
Index entries for sequences related to Egyptian fractions


EXAMPLE

1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/13 + 1/23 + 1/721 + 1/979011 + 1/175878510309 + 1/20622166925499467673345 = 1.


PROG

(PARI) f=0; n=3; s=11; if(s<11, break); for(t=1, s3, print1(n, ", "); f=f+1/n; until(1>f+1/n, n=n+2)); until(numerator(1f1/n)==2, n=n+2); print1(n, ", "); f=f+1/n; g=2*floor((numerator(f)+1)/4)+1; until(numerator(1f1/g)==1, g=g+2); print1(g, ", "); f=f+1/g; print1(denominator(1f));


CROSSREFS

Cf. A238795, A201646.
Sequence in context: A226484 A261213 A130738 * A024323 A118820 A117521
Adjacent sequences: A239033 A239034 A239035 * A239037 A239038 A239039


KEYWORD

nonn,fini,full,nice


AUTHOR

Arkadiusz Wesolowski, Mar 09 2014


STATUS

approved



