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A062328 Length of period of continued fraction expansion of square root of 3^n+1. 1
0, 1, 4, 1, 26, 1, 56, 1, 44, 1, 264, 1, 814, 1, 136, 1, 3730, 1, 20968, 1, 2448, 1, 287980, 1, 397238, 1, 2678, 1, 670896, 1, 8110044, 1, 20696, 1, 1066520, 1, 366601254, 1, 277444, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

The period of sqrt(244) contains 26 terms: [1, 1, 1, 1, 1, 2, 1, 5, 1, 1, 9, 1, 6, 1, 9, 1, 1, 5, 1, 2, 1, 1, 1, 1, 1, 30], so a(5) = 26.

MAPLE

with(numtheory): [seq(nops(cfrac(sqrt(3^k+1), 'periodic', 'quotients')[2]), k=2..18)];

MATHEMATICA

Table[Length[Last[ContinuedFraction[Sqrt[3^w+1]]]], {w, 1, 40}] (* Harvey P. Dale, Dec 05 2014 *)

CROSSREFS

Cf. A059866, A059926, A059927, A062682.

Sequence in context: A046860 A089505 A300083 * A263918 A136234 A196528

Adjacent sequences:  A062325 A062326 A062327 * A062329 A062330 A062331

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 13 2001

EXTENSIONS

More terms from and prior Mathematica program corrected by Harvey P. Dale, Dec 05 2014

STATUS

approved

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Last modified August 18 13:28 EDT 2018. Contains 313832 sequences. (Running on oeis4.)