A080634 - OEIS

A080634

Start with a(1)=1. Then, for n>1, choose a(n)=1 or 2 so as to minimize the longest arithmetic progression in either S1(n) or S2(n), where S1(n)={k|a(k)=1,1<=k<=n} and S2(n)={k|a(k)=2,1<=k<=n}.

1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

Given the first seven terms as {1,2,1,2,2,1,2}, we find that a(8)=1 gives S1(8)={1,3,6,8}, S2(8)={2,4,5,7}, both with maximum AP's of length 2, whereas a(8)=2 gives S1(8)={1,3,6}, S2(8)={2,4,5,7,8}, with max length AP's of 2 for S1 and 3 for S2. So a(8) must be assigned the value of 1.

CROSSREFS

Sequence in context: A025143 A174314 A237253 * A109925 A306260 A180227

Adjacent sequences: A080631 A080632 A080633 * A080635 A080636 A080637

KEYWORD

nonn

AUTHOR

John W. Layman, Feb 27 2003

STATUS

approved