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A370231
a(1) = 1; for n >= 2, a(n) = a(GCD(n - 1, a(n - 1))) + floor((n - 1)/a(n - 1)) + 1.
0
1, 3, 2, 3, 3, 3, 5, 3, 4, 4, 6, 3, 7, 3, 6, 5, 5, 5, 5, 5, 8, 4, 9, 4, 10, 6, 8, 5, 7, 6, 9, 5, 8, 6, 9, 5, 9, 6, 10, 5, 12, 5, 10, 6, 11, 6, 11, 6, 12, 6, 12, 7, 9, 7, 9, 8, 11, 7, 10, 7, 10, 8, 11, 7, 11, 7, 11, 8, 12, 8, 12, 7, 12, 8, 13, 7, 12, 8, 13, 8, 14, 7
OFFSET
1,2
COMMENTS
The sequence is growing approximately like sqrt(n). Periods of unrest are connected (see Formula section) with constant rope.
FORMULA
For n from [4*k^2, 4*k^2 + 2*k], a(n) = 2*k + 1 and k = floor(r^(3/2)), r >= 1.
EXAMPLE
a(1) = 1.
a(2) = a(GCD(1, a(1))) + floor(1/a(1)) + 1 = 1 + 1 + 1 = 3.
a(3) = a(GCD(2, a(2))) + floor(2/a(2)) + 1 = 1 + 0 + 1 = 2.
a(4) = a(GCD(3, a(3))) + floor(3/a(3)) + 1 = 1 + 1 + 1 = 3.
and so on.
CROSSREFS
Sequence in context: A205237 A086920 A182021 * A117451 A130970 A144733
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Feb 12 2024
STATUS
approved