login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(1)=1, a(2)=2; for n > 2, a(n) is the smallest unused positive number such that gcd(a(n-1) * |a(n-1) - a(n-2)|, a(n)) > 1.
3

%I #39 Jan 30 2022 19:31:56

%S 1,2,4,6,3,9,8,10,5,15,12,14,7,21,16,18,20,22,11,33,24,26,13,39,27,28,

%T 30,25,35,32,34,17,51,36,38,19,57,40,42,44,46,23,69,45,48,50,52,54,56,

%U 49,63,58,29,87,60,55,65,62,31,93,64,66,68,70,72,74,37,111,75,76,78,80,82,41,123,81

%N a(1)=1, a(2)=2; for n > 2, a(n) is the smallest unused positive number such that gcd(a(n-1) * |a(n-1) - a(n-2)|, a(n)) > 1.

%C This is likely a permutation of the natural numbers. The sequence shows similar behavior to the EKG sequence A064413. In the first 500000 terms the fixed points are 1, 2, 77, 221, and it is likely no more exist.

%H Scott R. Shannon, <a href="/A350927/a350927.png">Image of the first 10000 terms</a>. The green line is y = n.

%e a(4) = 6 as a(3)*|a(3)-a(2)| = 4*2 = 8, 6 has not been used and gcd(6,8) > 1.

%e a(8) = 10 as a(7)*|a(7)-a(6)| = 8*1 = 8, 10 has not been used and gcd(10,8) > 1.

%Y Cf. A351001, A337136, A064413, A336957, A098550, A089088, A251622.

%K nonn

%O 1,2

%A _Scott R. Shannon_, Jan 28 2022