

A069214


Let u(n,k) be the recursion defined by u(n,1)=1, u(n,2)=2, u(n,3)=n, and u(n,k+3) = (u(n,k+2) + u(n,k+1))/u(n,k) if u(n,k) divides u(n,k+2) + u(n,k+1), u(n,k+3) = u(n,k) otherwise. Then u(n,k) is periodic and a(n) = Max(u(n,k), k=1,2,3,4,...).


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5, 4, 5, 6, 8, 8, 11, 10, 14, 12, 17, 14, 20, 16, 23, 18, 26, 20, 29, 22, 32, 24, 35, 26, 38, 28, 41, 30, 44, 32, 47, 34, 50, 36, 53, 38, 56, 40, 59, 42, 62, 44, 65, 46, 68, 48, 71, 50, 74, 52, 77, 54, 80, 56, 83, 58, 86, 60, 89, 62, 92, 64, 95, 66, 97, 68, 100, 70, 103, 72
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OFFSET

1,1


COMMENTS

Let p(n) denote the period of u(n,k) (i.e., p(n) is the smallest integer such that u(n,k) = u(n, k+p(n))). p(n) = 22,12,22,21,15,9,15,9,15,9,... for n = 1,2,3,4,5,6,.... Hence for n > 4, p(n) = 15 if n is odd; p(n) = 9 if n is even.


LINKS

Table of n, a(n) for n=1..70.


FORMULA

a(1)=5, a(2n)=2n+2, a(2n+1)=3n+2.


EXAMPLE

E.g., for k=1..15, u(7, k) = 1, 2, 7, 9, 8, 7, 9, 2, 7, 1, 4, 7, 11, 4, 7; hence a(7)=11.


CROSSREFS

Sequence in context: A021651 A200293 A211006 * A119807 A254181 A245018
Adjacent sequences: A069211 A069212 A069213 * A069215 A069216 A069217


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Apr 11 2002


STATUS

approved



