The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A308720 The maximum value in the continued fraction of sqrt(n), or 0 if there is no fractional part. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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) = floor(sqrt(m)) for nonsquare m. a(n) = 2 * A320471(n) for n > 0. MATHEMATICA {0} ~Join~ Table[2 Mod[Floor@ Sqrt@ n, Ceiling@ Sqrt@ n], {n, 100}] (* Giovanni Resta, Jun 29 2019 *) CROSSREFS Cf. A000196, A003285, A096494. Sequence in context: A073469 A307076 A342472 * A086882 A341415 A328141 Adjacent sequences: A308717 A308718 A308719 * A308721 A308722 A308723 KEYWORD nonn,easy AUTHOR Karl Fischer, Jun 19 2019 EXTENSIONS More terms from Giovanni Resta, Jun 29 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 9 08:03 EDT 2024. Contains 375034 sequences. (Running on oeis4.)