A118201 Smallest difference such that both difference and number do not occur previously.

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 44, 68, 93, 66, 38, 67, 37, 5, 36, 69, 35, 70, 34, 71, 33, 72, 32, 73, 31, 74, 30, 75, 29, 76, 28, 77, 27, 78, 26, 79, 133, 188, 132, 189, 131, 190, 130, 191, 129, 192, 128, 193, 127, 60, 134

Offset

0,3

Comments

Similar to Recamán's sequence (A005132), but increases the difference to avoid duplicating values. Conjecture that every nonnegative integer occurs in this sequence. Evaluating through n=20000, the smallest number that has not occurred is 139.

The first 14 terms appear in the original OEIS logo. - Philippe Deléham, Mar 01 2013

This is very similar to A064389, and arguably just as nice. - Franklin T. Adams-Watters, Nov 11 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Formula

a(n+1) = a(n)-d or a(n)+d, where a(n+1) must be positive and must not have occurred previously in the sequence; choose the smallest positive d such that this is possible where d is not |a(m+1)-a(m)| for any m < n; if both a(n)-d and a(n)+d have not occurred, choose a(n)-d.

Maple

N:= 1000: # get all terms up to the first member > N
a[0]:= 0:
davail:= [$1..N]:
B:= Vector(2*N):
for n from 1 do
  found:= false;
  for i from 1 to nops(davail) do
    d:= davail[i];
    an:= a[n-1]-d;
    if an > 0 and B[an] = 0 then
      a[n]:= an; found:= true; break
    fi;
    ap:= a[n-1]+d;
    if B[ap] = 0 then
      a[n]:= ap; found:= true; break
    fi
  od:
  if (not found) or (a[n] > N) then break fi;
  davail:= subsop(i=NULL, davail);
  B[a[n]]:= 1;
od:
seq(a[i], i=0..n);  # Robert Israel, Nov 17 2015

Mathematica

M = 1000; (* get all terms up to the first member > M *)
a[0] = 0;
davail = Range[M];
B = Array[0&, 2M];
For[n = 1, True, n++,
found = False;
For[i = 1, i <= Length[davail], i++,
d = davail[[i]];
an = a[n-1] - d;
If[an > 0 && B[[an]] == 0,
a[n] = an; found = True; Break[]
];
ap = a[n-1] + d;
If[B[[ap]] == 0,
a[n] = ap; found = True; Break[]
]
];
If [Not @ found || (a[n] > M), Break[]];
davail = ReplacePart[davail, i -> Nothing];
B[[a[n]]] = 1;
];
Table[a[i], {i, 0, n}] (* Jean-François Alcover, Oct 24 2016, translated from Robert Israel's Maple code *)

Crossrefs

Cf. A118202 (inverse), A005132, A064389.

Sequence in context: A064388 A064387 A064389 * A274647 A113880 A339192

Adjacent sequences: A118198 A118199 A118200 * A118202 A118203 A118204

Keyword

nonn,look,nice

Author

Franklin T. Adams-Watters, Apr 14 2006

Status

approved