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 A206579 Numbers k such that the periodic part of the continued fraction of sqrt(k) has more ones than any smaller k. 1

%I

%S 2,3,7,13,43,94,133,211,244,478,604,886,1279,1516,1726,3004,3271,3436,

%T 4111,4846,4999,6484,6694,7606,9739,10399,10774,12919,13126,15031,

%U 16699,17599,17614,18379,19231,25516,25939,32839,32971,39526,40639,42046,42571

%N Numbers k such that the periodic part of the continued fraction of sqrt(k) has more ones than any smaller k.

%C The number 1 is the most common number in continued fractions of sqrt(k) for k = 1, 2, 3, ....

%C Most of the terms in this sequence are the product of a prime and a power of 2. There are only three exceptions less than 10^6: 133, 253621, and 375181.

%e The periodic part of the continued fraction of sqrt(7) is (1, 1, 1, 4), which has more ones than any smaller square root.

%t t = {{2, 0}}; Do[If[! IntegerQ[Sqrt[k]], cnt = Count[ContinuedFraction[Sqrt[k]][], 1]; If[cnt > t[[-1, 2]], AppendTo[t, {k, cnt}]]], {k, 3, 50000}]; Transpose[t][]

%Y Cf. A206578 (least number having exactly n ones in its continued fraction).

%Y Cf. A206580 (number of ones for a(n)).

%K nonn

%O 1,1

%A _T. D. Noe_, Feb 29 2012

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Last modified March 25 22:18 EDT 2023. Contains 361529 sequences. (Running on oeis4.)