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A131393 Conjectured permutation of the positive integers using Rule 2 with a(1)=1.

%I A131393 #21 May 31 2021 21:30:13
%S A131393 1,2,4,3,6,10,8,5,11,7,12,19,14,22,16,9,18,28,20,31,21,33,24,13,26,40,
%T A131393 27,42,30,15,32,48,34,17,35,54,38,58,39,60,37,59,41,64,44,23,47,25,50,
%U A131393 76,52,79,53,81,56,29,61,90,62,92,63,94,57,91,55,88,49,84,51,87,46,83
%N A131393 Conjectured permutation of the positive integers using Rule 2 with a(1)=1.
%C A131393 Conjecture 1: a( ) is a permutation of the positive integers. Conjecture 2: d( ) is a permutation of the integers. The sequence using Rule 1 ("negative before positive") is A131388.
%C A131393 This sequence was generated using "Rule 2" in a computer program which been lost. The wording of "Rule 2" in the Formula section, although flawed, is retained in case someone can rediscover "Rule 2" and contribute a corrected version. - _Clark Kimberling_, May 18 2015
%H A131393 <a href="/A131393/b131393.txt">Table of n, a(n) for n = 1..72</a>
%F A131393 The following version of "Rule 2" is defective; see Comments. - _Clark Kimberling_, May 18 2015
%F A131393 Rule 2 ("positive before negative"): define sequences d( ) and a( ) as follows: d(1)=0, a(1)=1 and for n>=2, d(n) is the least positive integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1), or, if no such d exists, then d(n) is the greatest negative integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1). Then a(n)=a(n-1)+d.
%e A131393 a(2)=1+1, a(3)=a(2)+2, a(4)=a(3)+(-1), a(5)=a(4)+3, a(6)=a(5)+4.
%e A131393 The first term that differs from A131388 is a(28)=42.
%Y A131393 Cf. A131388, A131389, A131390, A131391, A131392, A131394, A131395, A131396, A131397.
%K A131393 nonn,unkn
%O A131393 1,2
%A A131393 _Clark Kimberling_, Jul 05 2007