

A031417


Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 4.


1



274, 370, 481, 797, 953, 1069, 1249, 1313, 1378, 1381, 1514, 1657, 1658, 1733, 1889, 2125, 2297, 2377, 2554, 2557, 2833, 2834, 2929, 2941, 3226, 3329, 3338, 3433, 3541, 3761, 3874, 3989, 4093, 4106, 4441, 4442, 4561, 4682, 4685, 4933, 4937, 5197, 5450
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OFFSET

1,1


LINKS

T. D. Noe, Table of n, a(n) for n = 1..999


EXAMPLE

The simple continued fraction for sqrt(274) = [16; 1, 1, 4, 4, 1, 1, 32, ...] with odd period 7 and central term 4. Another example is sqrt(481) = [21; 1, 13, 1, 1, 1, 4, 4, 1, 1, 1, 13, 1, 42, ...] with odd period 13 and central term 4.  Michael Somos, Apr 03 2014


MATHEMATICA

n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 4, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 03 2014 *)


CROSSREFS

Cf. A031404A031423.
Sequence in context: A307537 A295455 A174771 * A260289 A322254 A204278
Adjacent sequences: A031414 A031415 A031416 * A031418 A031419 A031420


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

a(1) corrected by T. D. Noe, Apr 03 2014


STATUS

approved



