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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)). 2

%I

%S 3,7,11,13,21,29,39,39,49,69,67,69,69,79,83,87,81,101,111,115,133,141,

%T 139,151,187,157,191,187,199,213,223,211,221,241,255,275,309,293,287,

%U 279,295,293,303,283,325,345,357,367,403,393,419,419,477,457,519,487

%N 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)).

%C 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))

%F Conjecture : a(n)/n is bounded

%e 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

%K nonn

%O 1,1

%A _Benoit Cloitre_, Dec 03 2002

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Last modified October 21 05:06 EDT 2021. Contains 348141 sequences. (Running on oeis4.)