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A256701
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Positive part of the minimal alternating binary representation of n (defined at A245596).
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4
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1, 2, 4, 4, 9, 8, 8, 8, 17, 18, 20, 16, 17, 16, 16, 16, 33, 34, 36, 36, 41, 40, 40, 32, 33, 34, 36, 32, 33, 32, 32, 32, 65, 66, 68, 68, 73, 72, 72, 72, 81, 82, 84, 80, 81, 80, 80, 64, 65, 66, 68, 68, 73, 72, 72, 64, 65, 66, 68, 64, 65, 64, 64, 64, 129, 130
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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R(1) = 1; positive part 1, nonpositive part 0
R(2) = 2; positive part 2, nonpositive part 0
R(3) = 4 - 1; positive part 4, nonpositive part 1
R(11) = 16 - 8 + 4 - 1; positive part 16+4 = 20; nonpositive part 8 + 1 = 9
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MATHEMATICA
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b[n_] := 2^n; bb = Table[b[n], {n, 0, 40}];
s[n_] := Table[b[n + 1], {k, 1, b[n]}];
h[0] = {1}; h[n_] := Join[h[n - 1], s[n - 1]];
g = h[10]; Take[g, 100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
Table[Total[Abs[r[n]]], {n, 1, 100}] (* A073122 *)
u = Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 100}] (* A256701 *)
v = Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 100}] (* A256702 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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