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A099725 a(n) is the number of 1's in the period of the continued fraction of the square root of the n-th nonsquare integer. 2
0, 1, 0, 0, 3, 1, 0, 0, 0, 4, 2, 1, 0, 0, 2, 0, 4, 2, 2, 1, 0, 0, 0, 2, 0, 4, 3, 2, 2, 1, 0, 0, 0, 0, 0, 0, 6, 6, 2, 6, 2, 1, 0, 0, 2, 2, 2, 0, 0, 4, 6, 2, 2, 4, 2, 1, 0, 0, 4, 0, 2, 2, 2, 0, 4, 4, 3, 6, 2, 2, 2, 1, 0, 0, 0, 2, 6, 0, 3, 0, 0, 5, 4, 6, 8, 2, 2, 8, 2, 1, 0, 0, 6, 0, 0, 4, 2, 4, 4, 0, 4, 4, 6, 2, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

For sufficiently large period lengths, the fraction of 1's in the repeating part tends to log(4/3)/log(2) = 0.415... as from the Gauss-Kuzmin distribution, i.e., a(n) tends to 0.415...*A013943(n) for sufficiently large A013943(n). - A.H.M. Smeets, Jun 02 2018

The "n-th nonsquare integer" in the definition is A005117(n + 1). - Michael B. Porter, Jun 06 2018

LINKS

A.H.M. Smeets, Table of n, a(n) for n = 1..10000

CROSSREFS

Cf. A005117, A013647.

Sequence in context: A285631 A316836 A058612 * A285118 A128208 A154721

Adjacent sequences:  A099722 A099723 A099724 * A099726 A099727 A099728

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Nov 07 2004

STATUS

approved

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Last modified August 7 17:02 EDT 2020. Contains 336277 sequences. (Running on oeis4.)