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

2, 3, 7, 13, 43, 94, 133, 211, 244, 478, 604, 886, 1279, 1516, 1726, 3004, 3271, 3436, 4111, 4846, 4999, 6484, 6694, 7606, 9739, 10399, 10774, 12919, 13126, 15031, 16699, 17599, 17614, 18379, 19231, 25516, 25939, 32839, 32971, 39526, 40639, 42046, 42571

Offset: 1

Author

T. D. Noe, Feb 29 2012

Keywords

• nonn

Comments

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

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.

Examples

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

Crossrefs

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

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

Programs

Mathematica

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