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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; text; 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)? LINKS 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 Adjacent sequences: A134566 A134567 A134568 * A134570 A134571 A134572 KEYWORD nonn AUTHOR Clark Kimberling, Nov 02 2007 STATUS approved

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Last modified January 28 09:01 EST 2023. Contains 359851 sequences. (Running on oeis4.)