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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 16:06 EST 2023. Contains 360128 sequences. (Running on oeis4.)