

A065677


Maximal Diffy_length for quadruples of numbers <= n.


3



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, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13
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OFFSET

0,2


COMMENTS

For quadruples of nonnegative integers a, b, c, d we let diffy([a, b, c, d]) := [ab, bc, cd, da] (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]).
Monotonically nondecreasing; the sequence A065678 (or A045794) is its "inverse" (i.e. A065678(n) = min {m  A065677(m) >= n})


LINKS

Table of n, a(n) for n=0..72.
Raymond Greenwell, 73.35 The Game of Diffy, Math. Gazette, Vol. 73, No. 465 (Oct., 1989), pp. 222225.
Univ. Mass. Computer Science 121, The Diffy Game


EXAMPLE

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)


CROSSREFS

Cf. A065678 (or A045794).
Sequence in context: A203632 A278766 A320828 * A006672 A107287 A240119
Adjacent sequences: A065674 A065675 A065676 * A065678 A065679 A065680


KEYWORD

nonn


AUTHOR

Jens Voß, Nov 13 2001


STATUS

approved



