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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 (list; graph; refs; listen; history; internal format)
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}=.2426... for m=1 whereas

{-2*r}=.1715..., so that 2 is the least m for which

{-m*r}<{3*r}.

CROSSREFS

Cf. A134568.

Sequence in context: A126906 A179508 A134304 * A072883 A093101 A082469

Adjacent sequences:  A134566 A134567 A134568 * A134570 A134571 A134572

KEYWORD

nonn

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Nov 02 2007

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Last modified February 16 16:24 EST 2012. Contains 205938 sequences.