A370231 a(1) = 1; for n >= 2, a(n) = a(GCD(n - 1, a(n - 1))) + floor((n - 1)/a(n - 1)) + 1.

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.

Links

Table of n, a(n) for n=1..82.

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

Cf. A002024, A005206.

Sequence in context: A205237 A086920 A182021 * A117451 A130970 A144733

Adjacent sequences: A370228 A370229 A370230 * A370232 A370233 A370234

Keyword

nonn

Author

Ctibor O. Zizka, Feb 12 2024

Status

approved