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A064289 Height of n-th term in Recamán's sequence A005132. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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, Sep 08 2019
LINKS
EXAMPLE
A005132 begins 1, 3, 6, 2, 7, 13, 20, 12, ... and these terms have heights 1, 2, 3, 2, 3, 4, 5, 4, ...
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A209302 A205122 A174863 * A078759 A276439 A282701
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 25 2001
EXTENSIONS
a(0)=0 prepended by Allan C. Wechsler, Sep 08 2019
STATUS
approved

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Last modified April 16 22:23 EDT 2024. Contains 371755 sequences. (Running on oeis4.)