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A320063
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A sequence which changes by one or zero: a(n) = a(n-1-a(a(n-1))) + a(a(a(n-1))) for n > 1, a(n) = n for n < 2.
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2
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0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 16, 17, 17, 17, 17, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 22, 23, 23, 23, 24, 24, 25, 26, 27, 27, 27, 27, 27, 28, 28, 29, 29, 29
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OFFSET
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0,4
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COMMENTS
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This is similar to a problem that I had in the Monthly 35 years ago. The solution then was by Daniel Kleitman.
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LINKS
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n,
a(n-1-a(a(n-1)))+a(a(a(n-1))))
end:
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MATHEMATICA
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f[0] = 0;
f[1] = 1;
f[n_] := f[n] = +f[n - 1 - f[f[n - 1]]] + f[f[f[n - 1]]];
Table[f[i], {i, 1, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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