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A065677 Maximal Diffy_length for quadruples of numbers <= n.

%I A065677 #8 Oct 21 2017 16:20:55
%S A065677 0,4,4,6,7,7,7,7,7,8,8,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
%T A065677 10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,13,13,13,13,13,13,
%U A065677 13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13
%N A065677 Maximal Diffy_length for quadruples of numbers <= n.
%C A065677 For quadruples of nonnegative integers a, b, c, d we let diffy([a, b, c, d]) := [|a-b|, |b-c|, |c-d|, |d-a|] (i.e. the quadruple of absolute differences of neighboring values, cyclically speaking) and Diffy_length([a, b, c, d]) := min { n in N | diffy^n([a, b, c, d]) = [0, 0, 0, 0] } (i.e. the minimum number of diffy iterations needed to convert [a, b, c, d] into [0, 0, 0, 0]).
%C A065677 Monotonically nondecreasing; the sequence A065678 (or A045794) is its "inverse" (i.e. A065678(n) = min {m | A065677(m) >= n})
%H A065677 Raymond Greenwell, <a href="http://www.jstor.org/stable/3618447">73.35 The Game of Diffy</a>, Math. Gazette, Vol. 73, No. 465 (Oct., 1989), pp. 222-225.
%H A065677 Univ. Mass. Computer Science 121, <a href="http://www-unix.oit.umass.edu/~cs121/projects/project3/p3.htm">The Diffy Game</a>
%e A065677 Diffy_length([0,0,0,1]) = 4 since diffy^4([0,0,0,1]) = diffy^3([0,0,1,1]) = diffy^2([0,1,0,1]) = diffy([1,1,1,1]) = [0,0,0,0], so A065677(1) >= 4 (considering all quadruples of numbers 0 and 1 shows that in fact A065677(1) = 4)
%Y A065677 Cf. A065678 (or A045794).
%K A065677 nonn
%O A065677 0,2
%A A065677 _Jens Voß_, Nov 13 2001