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A308720

The maximum value in the continued fraction of sqrt(n), or 0 if there is no fractional part.

0, 0, 2, 2, 0, 4, 4, 4, 4, 0, 6, 6, 6, 6, 6, 6, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 16, 16, 16, 16, 16, 16, 16

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OFFSET

0,3

COMMENTS

The continued fraction expansion of sqrt(n) is periodic, and the maximal element is the last element in the period, 2*floor(sqrt(n)).

LINKS

Table of n, a(n) for n=0..71.

Oskar Perron, Die Lehre von den Kettenbrüchen, B. G. Teubner (1913), section 24, p. 87.

FORMULA

a(k^2) = 0.

a(m) = 2 * floor(sqrt(m)) for nonsquare m.

a(n) = 2 * A320471(n) for n > 0.