A078098 Let u(1)=u(2)=1, u(3)=2n+1, u(k)=abs(u(k-1)-u(k-2)-u(k-3)); then for any n (u(k),u(k+1)) = (v(n),w(n)) for k large enough; sequence gives values of Max(v(n),w(n)).

3, 7, 11, 13, 21, 29, 39, 39, 49, 69, 67, 69, 69, 79, 83, 87, 81, 101, 111, 115, 133, 141, 139, 151, 187, 157, 191, 187, 199, 213, 223, 211, 221, 241, 255, 275, 309, 293, 287, 279, 295, 293, 303, 283, 325, 345, 357, 367, 403, 393, 419, 419, 477, 457, 519, 487

Offset: 1

Author

Benoit Cloitre, Dec 03 2002

Keywords

• nonn

Comments

a(n) is necessarily odd. Starting with u(1)=u(2)=1 u(3)=2n then u(k) seems unbounded and there seems to be 2 integer values x(n) y(n) such that for any m>x(n), Max( u(k) : 1<=k<=m) = sqrtint(m+y(n))

Examples

			Map of 2*2+1=5 under u(k) is : 1->1->5 ->3->3->5->1->7->1->7>->1->7->1....Hence a(2)=Max(1,7)=7
		

Formula

Conjecture : a(n)/n is bounded