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

Author

Eric Angelini and Alois P. Heinz, May 21 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Eric Angelini, Derangements on the SeqFan list, May 21 2015.

Crossrefs

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

Programs

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 *)

Formula

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