A258137 Absolute first differences of the lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.

2, 4, 6, 8, 10, 12, 18, 14, 16, 28, 20, 22, 36, 24, 26, 48, 30, 32, 60, 34, 38, 68, 40, 42, 78, 44, 46, 86, 50, 52, 100, 54, 56, 108, 58, 62, 114, 66, 64, 70, 72, 140, 74, 76, 146, 80, 82, 156, 84, 88, 170, 90, 92, 180, 94, 96, 188, 98, 102, 194, 104, 106, 208

Offset

1,1

Comments

All terms are even.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

E. Angelini, Derangements on the SeqFan list, May 21 2015

Formula

a(n) = abs(A258136(n+1)-A258136(n)).

a(n) = 2*abs(A099004(n)).

Maple

b:= proc() false end:
g:= proc(n) option remember; local k;
      if n=1 then b(1):= true; 1
    else g(n-1); for k while b(k) or
         b(abs(g(n-1)-k)) by 2 do od;
         b(k), b(abs(g(n-1)-k)):= true$2; k
      fi
    end:
a:= n-> abs(g(n+1)-g(n)):
seq(a(n), n=1..101);

Mathematica

b[_] = False;
g[n_] := g[n] = Module[{k},
     If[n == 1, b[1] = True; 1,
     g[n-1]; For[k = 1, b[k] ||
     b[Abs[g[n-1] - k]], k += 2];
     {b[k], b[Abs[g[n-1] - k]]} = {True, True}; k]];
a[n_] := Abs[g[n+1] - g[n]];
Table[a[n], {n, 1, 101}] (* Jean-François Alcover, Aug 01 2021, after Alois P. Heinz *)

Crossrefs

Absolute first differences of A258136.

Cf. A099004, A257941, A257944.

Sequence in context: A320674 A022483 A100180 * A101814 A034090 A146344

Adjacent sequences: A258134 A258135 A258136 * A258138 A258139 A258140

Keyword

nonn

Author

Eric Angelini and Alois P. Heinz, May 21 2015

Status

approved