

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
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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 0additive.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000
E. Angelini et al., 0additive and first differences and followup messages on the SeqFan list, May 13 2015
Eric Weisstein's World of Mathematics, sAdditive 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(n1)k)) do od;
for i to n1 do s(a(i)+k):= true od;
b(k), b(abs(a(n1)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[n1]k]], k++]; For[i = 1, i <= n1, i++, s[a[i]+k] = True]; {b[k], b[Abs[a[n1]k]]} = {True, True}; k]];
Array[a, 101] (* JeanFrançois 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



