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A369281 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, A091255(a(n), a(n+1)) = 1.

%I A369281 #21 Jan 21 2024 13:53:20
%S A369281 1,2,3,4,5,7,6,11,8,9,13,10,19,12,21,15,14,17,16,23,22,25,18,31,20,35,
%T A369281 24,37,26,27,32,29,28,33,38,39,41,30,47,34,49,40,55,36,59,42,43,44,45,
%U A369281 50,51,52,53,56,57,61,46,67,48,69,54,73,58,79,60,81,62
%N A369281 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, A091255(a(n), a(n+1)) = 1.
%C A369281 In other words, the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive terms are coprime.
%C A369281 As the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive integers are not necessarily coprime (see A369317-A369318), the present sequence does not equal the identity map.
%C A369281 This sequence is a permutation of the positive integers with inverse A369282:
%C A369281 - we can always extend the sequence with some term of A014580 not yet in the sequence, hence the sequence is infinite, and all terms of A014580 appear in the sequence, in ascending order,
%C A369281 - for any k > 0, the first term >= A014580(k) is precisely A014580(k),
%C A369281 - if a(n) = A014580(k) for some n and the least value not among the first n terms, say u, is less than A014580(k), then a(n+1) = u,
%C A369281 - and eventually every integer will appear in the sequence.
%H A369281 Rémy Sigrist, <a href="/A369281/b369281.txt">Table of n, a(n) for n = 1..10000</a>
%H A369281 Rémy Sigrist, <a href="/A369281/a369281.png">Scatterplot of the first 2500 terms</a>.
%H A369281 Rémy Sigrist, <a href="/A369281/a369281.gp.txt">PARI program</a>.
%H A369281 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A369281 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A369281 (PARI) See Links section.
%Y A369281 See A369293 for a similar sequence.
%Y A369281 Cf. A014580, A091255, A369282 (inverse), A369317-A369318.
%K A369281 nonn,base
%O A369281 1,2
%A A369281 _Rémy Sigrist_, Jan 18 2024