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

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)