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A064289
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Height of n-th term in Recamán's sequence A005132.
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18
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0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 8, 7, 8, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7
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OFFSET
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0,3
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COMMENTS
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The height of a term in A005132 = number of addition steps - number of subtraction steps to produce it.
Partial sums of A160357. - Allan C. Wechsler, 08 Sep 2019
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..100000
Nick Hobson, Python program for this sequence
N. J. A. Sloane, FORTRAN program for A005132, A057167, A064227, A064228
Index entries for sequences related to Recamán's sequence
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EXAMPLE
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A005132 begins 1, 3, 6, 2, 7, 13, 20, 12, ... and these terms have heights 1, 2, 3, 2, 3, 4, 5, 4, ...
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MAPLE
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g:= proc(n) is(n=0) end:
b:= proc(n) option remember; local t;
if n=0 then 0 else t:= b(n-1)-n; if t<=0 or g(t)
then t:= b(n-1)+n fi; g(t):= true; t fi
end:
a:= proc(n) option remember; `if`(n=0, 0,
a(n-1)+signum(b(n)-b(n-1)))
end:
seq(a(n), n=0..120); # Alois P. Heinz, Sep 08 2019
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MATHEMATICA
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g[n_] := n == 0;
b[n_] := b[n] = Module[{t}, If[n == 0, 0, t = b[n - 1] - n; If[t <= 0 || g[t], t = b[n - 1] + n]; g[t] = True; t]];
a[n_] := a[n] = If[n == 0, 0, a[n - 1] + Sign[b[n] - b[n - 1]]];
a /@ Range[0, 100] (* Jean-François Alcover, Apr 11 2020, after Alois P. Heinz *)
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CROSSREFS
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Cf. A005132, A064288, A064290, A064292, A064293, A064294, A160357.
Sequence in context: A209302 A205122 A174863 * A078759 A276439 A282701
Adjacent sequences: A064286 A064287 A064288 * A064290 A064291 A064292
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Sep 25 2001
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EXTENSIONS
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a(0)=0 prepended by Allan C. Wechsler, 08 Sep 2019
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STATUS
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approved
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