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a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not appeared that is a divisor of (a(n-1) + a(n-2))*|a(n-1) - a(n-2)|.
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%I #7 Apr 27 2022 11:06:16

%S 1,2,3,5,4,9,13,8,7,15,11,26,37,21,16,185,39,14,25,33,29,31,6,925,19,

%T 12,217,41,22,57,35,23,24,47,71,48,17,65,32,97,43,10,53,63,20,83,103,

%U 30,73,4429,18,401,383,28,137,55,64,51,115,128,27,101,74,45,119,82,67,149,36,113,77

%N a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not appeared that is a divisor of (a(n-1) + a(n-2))*|a(n-1) - a(n-2)|.

%C The sequence is finite, the final term being a(160)=143. See the examples. The maximum value is a(110)=35941 while the fixed points are 1, 2, 3, 8, 11, 67.

%e a(6) = 9 as (a(5)+a(4))*|a(5)-a(4)| = (4+5)*|4-5| = 9, and 9 is the smallest unused number that is a divisor of 9. This is the first term that differs from A353006.

%e a(159) = 144, a(160) = 143. Therefore a(161) would be the smallest unused number that divides (143+144)*|143-144| = 287. The divisors are 1, 7, 41, 287, all of which have already appeared, so the sequence terminates.

%Y Cf. A353006, A337136, A352867, A352790, A350927.

%K nonn,fini

%O 1,2

%A _Scott R. Shannon_, Apr 22 2022