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%I #8 Mar 09 2023 06:18:02
%S 1,3,6,12,2,10,14,26,4,11,28,17,22,35,65,5,20,36,8,32,9,23,42,76,18,
%T 38,56,15,41,16,25,54,87,21,48,27,63,24,66,7,59,13,44,93,49,84,30,62,
%U 100,19,69,106,37,90,212,34,74,122,33,89,46,129,249,39,86,141,40,101,183,50,95,159,52
%N a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest positive number which has not appeared that shares a factor with |a(n-1) - a(n-2)| while the difference |a(n) - a(n-1)| is distinct from all previous differences |a(i) - a(i-1)|, i=2..n-1.
%C In the first 100000 terms the only fixed point is a(1) = 1; it is unknown if more exist. The sequence is conjectured to be a permutation of the positive integers.
%H Scott R. Shannon, <a href="/A359799/a359799.png">Image for n = 1..100000</a>. The green line is a(n) = n.
%e a(5) = 2 as |a(4) - a(3)| = |12 - 6| = 6, and 2 is the smallest unused number that shares a factor with 6 while the difference |2 - a(4)| = |2 - 12| = 10 is distinct from all previous differences.
%Y Cf. A361314, A337136, A354755, A354727, A354687, A354753, A353989, A354087, A352763.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Mar 07 2023
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