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Search: id:A065677
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| A065677 |
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Maximal Diffy_length for quadruples of numbers <= n. |
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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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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
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Raymond Greenwell, The Game of Diffy, Math. Gazette, Oct 1989, p. 222.
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LINKS
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Univ. Mass. Computer Science 121, The Diffy Game
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EXAMPLE
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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
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Cf. A065678 (or A045794).
Adjacent sequences: A065674 A065675 A065676 this_sequence A065678 A065679 A065680
Sequence in context: A049751 A113523 A132882 this_sequence A006672 A107287 A105790
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KEYWORD
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nonn
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AUTHOR
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Jens Voss (jens.voss(AT)poet.de), Nov 13 2001
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