Oh, and I wanted to make sure I said this: if it turns out that A192787 is wrong, then before we correct it, we should figure out what the existing sequence really is, because it's probably interesting and shouldn't be discarded. On Tue, Feb 19, 2013 at 4:49 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I see your point, but if 1/1 is permitted, then 1/2 + 1/2 should be permitted too, and that would make A(4) = 5, not 4.
On Tue, Feb 19, 2013 at 4:45 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
1/1 ?? R.
On Tue, 19 Feb 2013, Allan Wechsler wrote:
Let A(n) be the number of ways of expressing 4/n as the sum of three
integer reciprocals, where the mere permutation of a sum is regarded as not making a difference.
Plainly 4/1 = 4 cannot be expressed as the sum of three reciprocals, so A(1) = 0.
4/2 = 2 = 1/1 + 1/2 + 1/2, and there are no other solutions, so A(2) = 1.
4/3 = 1 + 1/4 + 1/12 = 1+ 1/6 + 1/6 = 1/2 + 1/2 + 1/3; I am pretty sure that A(3) = 3.
The Erdős–Straus conjecture is that A(n) > 0 for all n > 1.
Of course I wanted to know if A was in OEIS. I calculated a few more terms, and what I had was 0, 1, 3, 3, 2, 8 ... I was pretty confident in my enumeration, so I calculated enough entries, and discovered to my surprise that the sequence was missing.
Then I searched for "Straus", and quickly found A192787, which claims to be my A. The trouble is, A192787(4) = 4, and I say A(4) = 3.
Bear with me while I list my solutions, and then somebody tell me what I missed.
4/4 = 1, so the problem is to partition 1 into three reciprocals. I have the following solutions:
1/2 + 1/3 + 1/6 1/2 + 1/4 + 1/4 1/3 + 1/3 + 1/3
A192787 seems to be claiming that I missed one. Charles R. Greathouse IV was the sequence author, and I think he's a funster, so, Charles, if you're listening, can you tell me the missing dissection? ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
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