cp's OEIS Frontend

A363576 a(1) = 1, a(2) = 6; for n > 2, a(n) is the smallest positive number that has not yet appeared such that a(n) has a common factor with a(n-1), has no common factor with 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.

%I A363576 #7 Aug 14 2023 08:29:42
%S A363576 1,6,10,35,21,12,20,55,33,18,28,77,143,26,14,105,51,34,40,95,57,24,22,
%T A363576 187,85,15,36,52,65,45,42,68,221,39,63,56,38,171,75,115,46,74,111,69,
%U A363576 92,44,165,87,58,88,99,135,50,82,123,183,122,70,133,209,66,93,155,80,114,153,391,161,84
%N A363576 a(1) = 1, a(2) = 6; for n > 2, a(n) is the smallest positive number that has not yet appeared such that a(n) has a common factor with a(n-1), has no common factor with 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 A363576 This is a variation of A360519 where the difference between consecutive terms is distinct. See A360519 for further details.
%C A363576 In the first 100000 terms the only fixed points are 1, 585 and 3619, although it is possible more exist.
%H A363576 Scott R. Shannon, <a href="/A363576/b363576.txt">Table of n, a(n) for n = 1..10000</a>
%e A363576 a(11) = 28 as 28 shares 2 as a common factor with a(10) = 18 while sharing no common factor with a(9) = 33. Also the difference |28 - 18| = 10 is distinct from all previous differences. This is the first term to differ from A360519.
%Y A363576 Cf. A360519, A361102, A098550, A336957.
%K A363576 nonn
%O A363576 1,2
%A A363576 _Scott R. Shannon_, Jun 10 2023