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URL: https://oeis.org/A353082

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A353082
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)|.
1
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, 12, 217, 41, 22, 57, 35, 23, 24, 47, 71, 48, 17, 65, 32, 97, 43, 10, 53, 63, 20, 83, 103, 30, 73, 4429, 18, 401, 383, 28, 137, 55, 64, 51, 115, 128, 27, 101, 74, 45, 119, 82, 67, 149, 36, 113, 77
OFFSET
1,2
COMMENTS
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.
EXAMPLE
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.
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.
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Scott R. Shannon, Apr 22 2022
STATUS
approved