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A258136 Lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.

%I A258136 #19 Dec 23 2024 14:53:44
%S A258136 1,3,7,13,5,15,27,9,23,39,11,31,53,17,41,67,19,49,81,21,55,93,25,65,
%T A258136 107,29,73,119,33,83,135,35,89,145,37,95,157,43,109,45,115,187,47,121,
%U A258136 197,51,131,213,57,141,229,59,149,241,61,155,251,63,161,263,69
%N A258136 Lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.
%H A258136 Alois P. Heinz, <a href="/A258136/b258136.txt">Table of n, a(n) for n = 1..1000</a>
%H A258136 Eric Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-May/014890.html">Derangements</a> on the SeqFan list, May 21 2015.
%F A258136 a(n) = 2*A081145(n)-1.
%p A258136 b:= proc() false end:
%p A258136 a:= proc(n) option remember; local k;
%p A258136       if n=1 then b(1):= true; 1
%p A258136     else a(n-1); for k while b(k) or
%p A258136          b(abs(a(n-1)-k)) by 2 do od;
%p A258136          b(k), b(abs(a(n-1)-k)):= true$2; k
%p A258136       fi
%p A258136     end:
%p A258136 seq(a(n), n=1..101);
%t A258136 b[_] = False;
%t A258136 a[n_] := a[n] = Module[{k},
%t A258136      If[n == 1, b[1] = True; 1,
%t A258136      a[n-1]; For[k = 1, b[k] ||
%t A258136      b[Abs[a[n-1] - k]], k += 2];
%t A258136      {b[k], b[Abs[a[n-1] - k]]} = {True, True}; k]];
%t A258136 Table[a[n], {n, 1, 101}] (* _Jean-François Alcover_, Aug 01 2021, after _Alois P. Heinz_ *)
%Y A258136 Cf. A081145, A258137 (absolute first differences), A257941, A257944.
%K A258136 nonn
%O A258136 1,2
%A A258136 _Eric Angelini_ and _Alois P. Heinz_, May 21 2015