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

1,1

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.

Links

Table of n, a(n) for n=1..43.

Example

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

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]]

Crossrefs

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

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

Sequence in context: A046062 A096263 A007996 * A349327 A166945 A257393

Adjacent sequences: A206576 A206577 A206578 * A206580 A206581 A206582

Keyword

nonn

Author

T. D. Noe, Feb 29 2012

Status

approved