Favorable Numbers (Posted on 2006-11-02)

	Submitted by Gamer
Rating: 3.0000 (1 votes)
Solution:	(Hide)
There are different solutions, but one simple method uses the equation from the solution to Unit Fractions: 1/a=1/(a-1)-1/(a*(a-1)) By applying it successively to the last term of the sequence forming 1/2, 1/3, 1/6, strictly smaller fractions may be created, thus allowing n to be any number 3 or greater. For n=4, 1/2, 1/3, 1/7, 1/42; for n=5 1/2, 1/3, 1/7, 1/43, 1/1806; ... What is left to check is for n=1 and n=2. For n=1, the series 1 works, but for n=2, the only integers whose sum adds to 1 are 2 and 2, but they are not distinct, thus 2 is the only unfavorable number.

	Subject	Author	Date
	Puzzle Answer	K Sengupta	2022-05-09 21:38:45
	Me too, me too! But...	JLo	2006-11-02 13:42:05
	Inductive answer	Federico Kereki	2006-11-02 12:43:16
	Solution	Eric	2006-11-02 12:14:47
	Minimalist Answer / No Spoiler	Old Original Oskar!	2006-11-02 10:56:09