A257941 Lexicographically earliest sequence of positive integers such that the terms and their absolute first differences are all distinct and no term is the sum of two distinct earlier terms.

1, 3, 7, 12, 18, 26, 9, 20, 34, 24, 39, 55, 22, 45, 66, 28, 47, 72, 85, 49, 76, 108, 68, 99, 53, 82, 112, 70, 114, 149, 74, 122, 172, 93, 145, 203, 101, 160, 95, 162, 216, 118, 187, 224, 141, 214, 143, 235, 139, 195, 281, 164, 241, 329, 166, 260, 170, 283, 168

Offset

1,2

Comments

The sequence of absolute first differences begins: 2, 4, 5, 6, 8, 17, 11, 14, 10, 15, 16, 33, 23, 21, 38, 19, 25, 13, 36, 27, 32, 40, ... .

The sequence is 0-additive.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

E. Angelini et al., 0-additive and first differences and follow-up messages on the SeqFan list, May 13 2015

Eric Weisstein's World of Mathematics, s-Additive Sequence

Maple

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

Mathematica

s[_] = False; b[_] = False;
a[n_] := a[n] = Module[{i, k}, If[n == 1, b[1] = True; 1, For[k = 1, b[k] || s[k] || Function[t, b[t] || t == k][Abs[a[n-1]-k]], k++]; For[i = 1, i <= n-1, i++, s[a[i]+k] = True]; {b[k], b[Abs[a[n-1]-k]]} = {True, True}; k]];
Array[a, 101] (* Jean-François Alcover, Oct 28 2020, after Maple *)

Crossrefs

Cf. A005228, A030124, A033627, A095115, A140778, A257944.

Sequence in context: A055998 A066379 A024517 * A257944 A005228 A000969

Adjacent sequences: A257938 A257939 A257940 * A257942 A257943 A257944

Keyword

nonn,look

Author

Eric Angelini and Alois P. Heinz, May 13 2015

Status

approved