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A134569
a(n) = least m such that {-m*r} < {n*r}, where { } denotes fractional part and r = sqrt(2).
1
2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 70, 2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 41, 2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 12, 2, 1, 2, 1, 7, 2, 1, 2, 1, 2, 1, 70, 2
OFFSET
1,1
COMMENTS
The defining inequality {-m*r} > {n*r} is equivalent to {m*r} + {n*r} < 1. Are all a(n) in A084068? Are all a(n) denominators of intermediate convergents to sqrt(2)?
EXAMPLE
a(3)=2 because {-m*r} < {3*r} = 0.2426... for m=1 whereas
{-2*r} = 0.1715..., so that 2 is the least m for which
{-m*r} < {3*r}.
CROSSREFS
Cf. A134568.
Sequence in context: A179508 A134304 A211096 * A295853 A287541 A288196
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 02 2007
STATUS
approved