20201017, 21:55  #441  
Feb 2017
Nowhere
2^{2}·3·5^{2}·13 Posts 
Quote:
Your offering 3,560,600,696,674 has AFAIK defied analysis so far (I haven't figured out why it is special), so you're current. 

20201017, 23:32  #442  
Jul 2018
Martin, Slovakia
271 Posts 
Quote:
1. It is a sum of a part of an infinite series of numbers 2. The series is related to the graph theory 

20201101, 10:37  #443 
Dec 2008
you know...around...
3·7·29 Posts 
Hmm... I wanted to post a new number, but still can't figure out Viliam Furik's number.
And I don't know much about graph theory either. 
20201101, 21:46  #444 
Feb 2017
Nowhere
2^{2}·3·5^{2}·13 Posts 
I'm afraid the hints haven't been enough for me, either. I don't know much about graph theory.
In particular, I don't know why adding the terms of a graphrelated sequence would be of significance. 
20201101, 22:37  #445 
Jul 2018
Martin, Slovakia
271 Posts 
First of all, I admit the number is not as special as other numbers I could have chosen.
3,560,600,696,674  number of tree graphs with at most 35 vertices. The specialness of this number lies in the Graceful Tree Conjecture, which states that all trees are graceful (there exists at least one graceful labelling for every tree graph). It has been verified by computers for all trees with at most 35 vertices. So far, every tree checked has at least one graceful labelling. This conjecture is of particular interest to me because I am trying to prove it, together with my schoolmate, but also because 6 mathematicians that have participated in its research were from Slovakia, namely Anton Kotzig and Alexander Rosa (these two, together with Gerhard Ringel, are the ones that conjectured it), Alfonz Haviar and Pavel Hrnčiar (published a result that every tree with a diameter at most 5 is graceful), and Miroslav Haviar and Michal Ivaška.  EDIT: I give up my turn to choose a new number. Last fiddled with by Viliam Furik on 20201101 at 22:45 
20201102, 00:44  #446  
Feb 2017
Nowhere
2^{2}·3·5^{2}·13 Posts 
Quote:
We want the number of "different" trees with n vertices. OK, got it. OEIS A000055. Number of trees with n unlabeled nodes. Enough terms to verify the total are given at A000055 as a simple table. 

20201113, 04:50  #447 
Jan 2012
Toronto, Canada
2×23 Posts 
66600049

20201113, 09:02  #448 
Romulan Interpreter
Jun 2011
Thailand
8963_{10} Posts 
Not fun, it is the first link gugu gives.
(however, we learned a couple of things from it! thanks for sharing, but the search was indeed not fun haha, too easy) Last fiddled with by LaurV on 20201113 at 09:03 
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