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The 1-2-3 Conjecture and related problems: a survey
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there is hope that not only is the conjecture of Hales, Moy, and Prasad true, ... I thank Je Adler for his comments on an earlier version of ... O. and the cardinality of O(0) is ve. 2.2 Some ltrations for SL. 2(F ). 2.2.1 Standard congruence ltration ... Moy and Prasad in [3, 4] have de ned a way to associate a lattice gx;r in g to. |
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Collatz Problem -- from Wolfram MathWorld
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As I understand it, an assumption is to take something for granted, whereas a ... and have a conjecture like this: _First, +3 then +5 then +7 then +9 then +11_. ... And you'll notice it agrees with the formula n^2 - 1 that Jill conjectured in Sal's video. I'm ... 2 Votes. • 1 Comment • Flag. 2014-07-12T19:22:31Z by Daniel S... |
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The 1,2,3-Conjecture and the 1,2-Conjecture
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A000045 - OEIS
0,4. COMMENTS. Also called Lamé's sequence. F(n+2) = number of binary ... F(n ) = number of permutations p of 1,2,3,... ,n such that |k-p(k)|<=1 for k=1,2,... ,n. ... . A weak ascent in a Motzkin path is a maximal sequence of consecutive U and H steps. ... Two conjectures: For n > 1, F(n+2)^2 mod F(n+1)^2 = F(n)*F(n+1) - (-1)^ n. |
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A001792 - OEIS
0,2. COMMENTS. Number of parts in all compositions (ordered partitions) of n + 1 . For example, a(2) = 8 because in 3 = 2 + 1 = 1 + 2 = 1 + 1 + 1 we ... Then a(n-1) + A098156(n+1) = 2*a(n) (conjecture). ... . G.f.: 1 + 2*x*U(0) where U(k) = 1 + (k + 1)/(2 - 8*x/(4*x + (k + 1)/U(k + 1))); (continued fraction, 3 - step). |