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A355065 Lexicographically earliest sequence of distinct positive integers such that if m and n are distinct and not coprime, then a(n) does not belong to the interval ceiling(a(m)/2)..2*a(m).

%I A355065 #10 Jun 22 2022 13:48:49
%S A355065 1,2,3,5,4,11,6,23,24,47,7,95,8,191,192,383,9,767,10,1535,1536,3071,
%T A355065 12,6143,3072,12287,12288,24575,13,49151,14,98303,98304,196607,98305,
%U A355065 393215,15,786431,786432,1572863,16,3145727,17,6291455,6291456,12582911,18
%N A355065 Lexicographically earliest sequence of distinct positive integers such that if m and n are distinct and not coprime, then a(n) does not belong to the interval ceiling(a(m)/2)..2*a(m).
%C A355065 This sequence is a permutation of the nonnegative integers (when n is prime, a(n) is the least value not yet in the sequence).
%C A355065 The inverse sequence (A355066) has similarities with the Two-Up sequence (A090252) as A355066(n) is coprime to the next n terms (and to the floor(n/2) previous terms).
%C A355065 Note that the relation "u does not belong to the interval ceiling(v/2)..2*v" is symmetrical (for u, v > 0).
%H A355065 Rémy Sigrist, <a href="/A355065/a355065.gp.txt">PARI program</a>
%H A355065 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A355065 The first terms, alongside the forbidden values, are:
%e A355065   n   a(n)  Forbidden values
%e A355065   --  ----  ---------------------------------------------------
%e A355065    1     1  None
%e A355065    2     2  None
%e A355065    3     3  None
%e A355065    4     5  1..4 (from m=2)
%e A355065    5     4  None
%e A355065    6    11  1..4 (from m=2), 2..6 (from m=3), 3..10 (from m=4)
%e A355065    7     6  None
%e A355065    8    23  1..4 (from m=2), 3..10 (from m=4), 6..22 (from m=6)
%e A355065    9    24  2..6 (from m=3), 6..22 (from m=6)
%e A355065   10    47  1..4 (from m=2), 3..10 (from m=4), 2..8 (from m=5),
%e A355065             6..22 (from m=6), 12..46 (from m=8)
%e A355065   11     7  None
%o A355065 (PARI) See Links section.
%Y A355065 Cf. A090252, A355066 (inverse).
%K A355065 nonn
%O A355065 1,2
%A A355065 _Rémy Sigrist_, Jun 17 2022