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A369293 Lexicographically earliest sequence of distinct positive integers such that a(1) = 1, a(2) = 2, and for any n > 1, A091255(a(n), a(n+1)) <> 1.

%I A369293 #17 Jan 21 2024 13:54:07
%S A369293 1,2,4,6,3,5,9,7,14,8,10,12,15,17,18,16,20,22,11,29,23,13,26,24,27,21,
%T A369293 28,30,32,34,33,31,62,36,35,42,38,19,53,39,40,43,25,50,44,46,45,48,51,
%U A369293 54,49,56,52,57,58,60,63,65,66,64,68,70,72,71,61,122,74
%N A369293 Lexicographically earliest sequence of distinct positive integers such that a(1) = 1, a(2) = 2, and for any n > 1, A091255(a(n), a(n+1)) <> 1.
%C A369293 In other words, the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive terms (beyond the initial term) are not coprime.
%C A369293 This sequence is a variant of the EKG sequence (A064413).
%C A369293 Is this a permutation of the positive integers?
%H A369293 Rémy Sigrist, <a href="/A369293/b369293.txt">Table of n, a(n) for n = 1..10000</a>
%H A369293 Rémy Sigrist, <a href="/A369293/a369293.png">Scatterplot of the first 100000 terms</a>
%H A369293 Rémy Sigrist, <a href="/A369293/a369293.gp.txt">PARI program</a>
%H A369293 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A369293 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%e A369293 The first terms, alongside A091255(a(n), a(n+1)), are:
%e A369293   n   a(n)  A091255(a(n), a(n+1))
%e A369293   --  ----  ---------------------
%e A369293    1     1                      1
%e A369293    2     2                      2
%e A369293    3     4                      2
%e A369293    4     6                      3
%e A369293    5     3                      3
%e A369293    6     5                      3
%e A369293    7     9                      7
%e A369293    8     7                      7
%e A369293    9    14                      2
%e A369293   10     8                      2
%o A369293 (PARI) See Links section.
%Y A369293 See A369281 and A369294 for similar sequences.
%Y A369293 Cf. A064413, A091255, A369302.
%K A369293 nonn,base
%O A369293 1,2
%A A369293 _Rémy Sigrist_, Jan 18 2024