A258136 Lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.

1, 3, 7, 13, 5, 15, 27, 9, 23, 39, 11, 31, 53, 17, 41, 67, 19, 49, 81, 21, 55, 93, 25, 65, 107, 29, 73, 119, 33, 83, 135, 35, 89, 145, 37, 95, 157, 43, 109, 45, 115, 187, 47, 121, 197, 51, 131, 213, 57, 141, 229, 59, 149, 241, 61, 155, 251, 63, 161, 263, 69

Offset

1,2

Links

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

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

Formula

a(n) = 2*A081145(n)-1.

Maple

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

Mathematica

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

Crossrefs

Cf. A081145, A258137 (absolute first differences), A257941, A257944.

Sequence in context: A346154 A010260 A366999 * A209387 A128156 A108768

Adjacent sequences: A258133 A258134 A258135 * A258137 A258138 A258139

Keyword

nonn

Author

Eric Angelini and Alois P. Heinz, May 21 2015

Status

approved