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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 (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

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

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Last modified February 23 08:00 EST 2019. Contains 320420 sequences. (Running on oeis4.)