|
%I #7 Feb 12 2024 10:32:30
%S 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,
%T 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,
%U 7,11,7,11,8,12,8,12,7,12,8,13,7,12,8,13,8,14,7
%N a(1) = 1; for n >= 2, a(n) = a(GCD(n - 1, a(n - 1))) + floor((n - 1)/a(n - 1)) + 1.
%C The sequence is growing approximately like sqrt(n). Periods of unrest are connected (see Formula section) with constant rope.
%F For n from [4*k^2, 4*k^2 + 2*k], a(n) = 2*k + 1 and k = floor(r^(3/2)), r >= 1.
%e a(1) = 1.
%e a(2) = a(GCD(1, a(1))) + floor(1/a(1)) + 1 = 1 + 1 + 1 = 3.
%e a(3) = a(GCD(2, a(2))) + floor(2/a(2)) + 1 = 1 + 0 + 1 = 2.
%e a(4) = a(GCD(3, a(3))) + floor(3/a(3)) + 1 = 1 + 1 + 1 = 3.
%e and so on.
%Y Cf. A002024, A005206.
%K nonn
%O 1,2
%A _Ctibor O. Zizka_, Feb 12 2024
|
