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Search: id:A131624
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| A131624 |
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Triangular array read by rows: a(1, n) = Mod[n, 10]; a(m, 1) = a(m - 1, 2); a(m, n) = Mod[a(m - 1, a(m, n - 1) + 1), 9]. |
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+0
1
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| 1, 2, 2, 3, 3, 3, 5, 5, 4, 4, 4, 4, 7, 5, 5, 8, 8, 2, 0, 6, 6, 2, 2, 2, 7, 2, 7, 7, 2, 2, 2, 2, 8, 4, 8, 8, 2, 2, 2, 2, 2, 1, 6, 0, 9, 2, 2, 2, 2, 2, 2, 5, 8, 1, 0
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A double-modulus Ackermann recursion.
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REFERENCES
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Harry R. Lewis and Christos H. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981, pages 296 and 345
Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, p. 906, 2002.
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LINKS
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Erc Weisstein, Ackermann Function
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FORMULA
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a(1, n) = Mod[n, 10]; a(m, 1) = a(m - 1, 2); a(m, n) = Mod[a(m - 1, a(m, n - 1) + 1), 9]; aout(n,m)=AntidiagonalTransform(a(n,m))
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EXAMPLE
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{1},
{2, 2},
{3, 3, 3},
{5, 5, 4, 4},
{4, 4, 7, 5, 5},
{8, 8, 2, 0, 6, 6},
{2, 2, 2, 7, 2, 7, 7},
{2, 2, 2, 2, 8, 4, 8, 8},
{2, 2, 2, 2, 2, 1, 6, 0, 9},
{2, 2, 2, 2, 2, 2, 5, 8, 1, 0}
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MATHEMATICA
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Clear[f] f[1, n_] := Mod[n, 10]; f[m_, 1] := f[m - 1, 2]; f[m_, n_] := Mod[f[m - 1, f[m, n - 1] + 1], 9]; a0 = Table[f[a, b], {a, 1, 10}, {b, 1, 10}]; ListDensityPlot[%, ColorFunction -> (Hue[2# ] &)]; Dimensions[a0]; (* antidiagonal transform*) c = Delete[Table[Reverse[Table[a0[[n, l - n]], {n, 1, l - 1}]], {l, 1, Dimensions[a0][[1]] + 1}], 1]; Flatten[c]
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CROSSREFS
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Cf. A001695/M2352 and A014221.
Sequence in context: A125843 A127332 A087826 this_sequence A063905 A130312 A076272
Adjacent sequences: A131621 A131622 A131623 this_sequence A131625 A131626 A131627
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KEYWORD
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nonn,tabl,easy,more
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 02 2007
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EXTENSIONS
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Edited by njas, Feb 02 2008
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