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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)