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A350927
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
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, 30, 25, 35, 32, 34, 17, 51, 36, 38, 19, 57, 40, 42, 44, 46, 23, 69, 45, 48, 50, 52, 54, 56, 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
OFFSET
1,2
COMMENTS
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.
LINKS
Scott R. Shannon, Image of the first 10000 terms. The green line is y = n.
EXAMPLE
a(4) = 6 as a(3)*|a(3)-a(2)| = 4*2 = 8, 6 has not been used and gcd(6,8) > 1.
a(8) = 10 as a(7)*|a(7)-a(6)| = 8*1 = 8, 10 has not been used and gcd(10,8) > 1.
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jan 28 2022
STATUS
approved