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A013648 Numbers k such that the periodic part of the continued fraction for sqrt(k) contains a single 1. 4
3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 175, 176, 195, 208, 224, 255, 288, 323, 360, 399, 440, 483, 528, 551, 575, 624, 675, 728, 783, 799, 840, 899, 960, 1023, 1035, 1088, 1155, 1224, 1247, 1295, 1368, 1403, 1443, 1520, 1599, 1680, 1763, 1848, 1872 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All the terms of A005563 are here, as well as some additional terms (with even period > 2 and the digit 1 in central position) (e.g., sqrt(175) = [13,'4, 2, 1, 2, 4, 26']).
REFERENCES
Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).
LINKS
R. Macmillan, Continued fractions, Math. Gaz. 84, 2000. See p. 34.
MATHEMATICA
Select[ Range@ 1900, !IntegerQ[ Sqrt@ #] && Count[ ContinuedFraction[ Sqrt@ #][[2]], 1] == 1 &] (* Robert G. Wilson v, Jul 03 2011 *)
CROSSREFS
Union of A005563 and A102538.
Sequence in context: A086959 A335753 A083656 * A258837 A131386 A132411
KEYWORD
nonn
AUTHOR
EXTENSIONS
Additional comments from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 30 2001
Incorrect formulas and programs removed by R. J. Mathar, Jan 06 2011
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)