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%I #11 May 10 2017 23:43:54
%S 1,3,5,7,11,13,9,15,17,19,23,25,29,27,31,21,37,35,33,39,41,43,47,49,
%T 53,45,55,51,59,61,67,57,71,63,73,65,79,69,77,81,83,85,75,87,89,91,97,
%U 95,101,93,103,99,107,109,113,111,115,105,119,121,127,117,125
%N Lexicographically earliest sequence of distinct positive terms such that for any n>0, i > j >=0, gcd(a^i(n), a^j(n)) = 1 (where a^k denotes the k-th iteration of a).
%C For any n>0, n and a(n) are coprime.
%C There is only one fixed point: a(1) = 1.
%C All terms are odd.
%C All terms > 1 have an even ancestor (if n > 1 then a(n) = a^i(2*j) for some i >= 0 and j > 0).
%C If n > 1, then a(n) > n.
%C This can be proved by induction, by considering u(n) = least odd term not seen among {a(1), ..., a(n-1)}, and noticing also that u(2*n) > 2*n.
%C The derived sequence b=(a+1)/2 is a permutation of the natural numbers.
%C The first terms of the orbit of 2 are: 2, 3, 5, 11, 23, 47, 97, 197, 401, 809, 1627, 3259, 61*107, 13063, 7*3733, 13*4021, 19*5503, 163*1283, 29*14423, 83*10079, 929*1801.
%C Conjecturally, a(n) ~ 2*n.
%H Rémy Sigrist, <a href="/A285848/b285848.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A285848/a285848.gp.txt">PARI program for A285848</a>
%e a(1) = 1 is appropriate.
%e a(2) must be coprime to 2, and differ from 1; a(2) = 3 is appropriate.
%e a(3) must be coprime to 3 and 2, and differ from 1 and 3; a(3) = 5 is appropriate.
%e a(4) must be coprime to 4, and differ from 1, 3 and 5; a(4) = 7 is appropriate.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Apr 27 2017
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