A064289 Height of n-th term in Recamán's sequence A005132.

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

Offset: 0

Author

N. J. A. Sloane, Sep 25 2001

Keywords

• nonn
• easy

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

Examples

			A005132 begins 1, 3, 6, 2, 7, 13, 20, 12, ... and these terms have heights 1, 2, 3, 2, 3, 4, 5, 4, ...
		

Links

• 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

Crossrefs

Cf. A005132, A064288, A064290, A064292, A064293, A064294, A160357.

Programs

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 *)

Extensions

a(0)=0 prepended by Allan C. Wechsler, Sep 08 2019