A257944 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 terms.

1, 3, 7, 12, 18, 26, 16, 31, 20, 37, 50, 22, 41, 64, 35, 56, 83, 39, 69, 45, 54, 79, 111, 58, 92, 130, 60, 96, 136, 73, 115, 163, 75, 121, 168, 77, 134, 193, 98, 149, 182, 102, 157, 206, 117, 178, 244, 138, 210, 277, 140, 214, 282, 153, 229, 307, 155, 220, 263

Offset

1,2

Comments

The sequence of absolute first differences begins: 2, 4, 5, 6, 8, 10, 15, 11, 17, 13, 28, 19, 23, 29, 21, 27, 44, 30, 24, 9, 25, 32, 53, ... .

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

Maple

s:= proc() false end: b:= proc() false end:
a:= proc(n) option remember; local i, k, ok;
      if n=1 then b(1):= true; 1
    else for k do if b(k) or s(k) or (t-> b(t) or t=k)(
           abs(a(n-1)-k)) then next fi; ok:=true;
           for i to n-1 while ok do if b(k+a(i))
             then ok:=false fi od; if ok then break fi
         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, ok}, If[n == 1, b[1] = True; 1,
     For[k = 1, True, k++, If[b[k] || s[k] || Function[t, b[t] ||
     t == k][Abs[a[n-1] - k]], Continue[]]; ok = True;
             For[i = 1, i <= n-1 && ok, i++, If[b[k + a[i]],
             ok = False]]; If[ok, Break[]]];
          For[i = 1, i <= n-1, i++, s[a[i] + k] = True];
          {b[k], b[Abs[a[n-1] - k]]} = {True, True}; k]];
Table[a[n], {n, 1, 101}] (* Jean-François Alcover, Jul 16 2021, after Alois P. Heinz *)

Crossrefs

Cf. A005228, A030124, A095115, A140778, A257941.

Sequence in context: A066379 A024517 A257941 * A005228 A000969 A194117

Adjacent sequences: A257941 A257942 A257943 * A257945 A257946 A257947

Keyword

nonn

Author

Eric Angelini and Alois P. Heinz, May 13 2015

Status

approved