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A065677
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Maximal Diffy_length for quadruples of numbers <= n.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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]).
Monotonically nondecreasing; the sequence A065678 (or A045794) is its "inverse" (i.e. A065678(n) = min {m | A065677(m) >= n})
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REFERENCES
| Raymond Greenwell, The Game of Diffy, Math. Gazette, Oct 1989, p. 222.
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LINKS
| Univ. Mass. Computer Science 121, The Diffy Game
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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)
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CROSSREFS
| Cf. A065678 (or A045794).
Sequence in context: A132882 A171384 A203632 * A006672 A107287 A200267
Adjacent sequences: A065674 A065675 A065676 * A065678 A065679 A065680
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KEYWORD
| nonn
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AUTHOR
| Jens Voss (jens.voss(AT)poet.de), Nov 13 2001
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