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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-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

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