

A013648


Numbers n such that period of continued fraction for sqrt(n) 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
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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, AddisonWesley, 1984, page 426 (but beware of errors!).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
R. Macmillan, Continued fractions, Math. Gaz. 84, 2000. See p. 34.


FORMULA

Union of A005563 and A102538.


MATHEMATICA

Select[ Range@ 1900, !IntegerQ[ Sqrt@ #] && Count[ ContinuedFraction[ Sqrt@ #][[2]], 1] == 1 &] (* Robert G. Wilson v, Jul 03 2011 *)


CROSSREFS

Cf. A040001, A040005, A040011, A040019, A040029, A062196.
Sequence in context: A191414 A086959 A083656 * A258837 A131386 A132411
Adjacent sequences: A013645 A013646 A013647 * A013649 A013650 A013651


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

Additional comments from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 30 2001
Incorrect formulas and programs removed  R. J. Mathar, Jan 06 2011


STATUS

approved



