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A258137 Absolute first differences of the lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.

%I A258137 #16 Dec 23 2024 14:53:44
%S A258137 2,4,6,8,10,12,18,14,16,28,20,22,36,24,26,48,30,32,60,34,38,68,40,42,
%T A258137 78,44,46,86,50,52,100,54,56,108,58,62,114,66,64,70,72,140,74,76,146,
%U A258137 80,82,156,84,88,170,90,92,180,94,96,188,98,102,194,104,106,208
%N A258137 Absolute first differences of the lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.
%C A258137 All terms are even.
%H A258137 Alois P. Heinz, <a href="/A258137/b258137.txt">Table of n, a(n) for n = 1..1000</a>
%H A258137 E. 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 A258137 a(n) = abs(A258136(n+1)-A258136(n)).
%F A258137 a(n) = 2*abs(A099004(n)).
%p A258137 b:= proc() false end:
%p A258137 g:= proc(n) option remember; local k;
%p A258137       if n=1 then b(1):= true; 1
%p A258137     else g(n-1); for k while b(k) or
%p A258137          b(abs(g(n-1)-k)) by 2 do od;
%p A258137          b(k), b(abs(g(n-1)-k)):= true$2; k
%p A258137       fi
%p A258137     end:
%p A258137 a:= n-> abs(g(n+1)-g(n)):
%p A258137 seq(a(n), n=1..101);
%t A258137 b[_] = False;
%t A258137 g[n_] := g[n] = Module[{k},
%t A258137      If[n == 1, b[1] = True; 1,
%t A258137      g[n-1]; For[k = 1, b[k] ||
%t A258137      b[Abs[g[n-1] - k]], k += 2];
%t A258137      {b[k], b[Abs[g[n-1] - k]]} = {True, True}; k]];
%t A258137 a[n_] := Abs[g[n+1] - g[n]];
%t A258137 Table[a[n], {n, 1, 101}] (* _Jean-François Alcover_, Aug 01 2021, after _Alois P. Heinz_ *)
%Y A258137 Absolute first differences of A258136.
%Y A258137 Cf. A099004, A257941, A257944.
%K A258137 nonn
%O A258137 1,1
%A A258137 _Eric Angelini_ and _Alois P. Heinz_, May 21 2015