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

Offset: 1

Author

Arkadiusz Wesolowski, Mar 09 2014

Keywords

• nonn
• fini
• full
• nice

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

Examples

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

Links

• D. R. Curtiss, On Kellogg's Diophantine problem, Amer. Math. Monthly 29 (1922), pp. 380-387.
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A238795, A201646.

Programs

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));