A078098 - OEIS

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

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OFFSET

1,1

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))

LINKS

Table of n, a(n) for n=1..56.

FORMULA

Conjecture : a(n)/n is bounded

EXAMPLE

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

CROSSREFS

Sequence in context: A310199 A176800 A176797 * A154831 A206944 A206943

Adjacent sequences: A078095 A078096 A078097 * A078099 A078100 A078101

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Dec 03 2002

STATUS

approved