A215485 Periods, n, of square root continued fractions at which A013646 increases.

0, 1, 2, 3, 7, 9, 13, 19, 23, 27, 35, 41, 43, 45, 53, 55, 71, 77, 101, 127, 129, 135, 147, 163, 169, 189, 199, 201, 247, 283, 335, 353, 367, 459, 465, 503, 537, 587, 625, 637, 643, 739, 767, 827, 1009, 1135, 1325, 1423, 1433, 1543, 1561

Offset

0,3

Comments

Each term of this sequence takes a turn at being the smallest unknown period for a square root continued fraction. Periods 1 and 2 are seen as the periods of sqrt(2) and sqrt(3) respectively, but a period of 3 is not seen until sqrt(41).

By convention, the period for perfect squares (e.g., 1) is 0.

Open question: Are there any more even terms after the 2?

Links

Patrick McKinley, Table of n, a(n) for n = 0..254

Example

When a square root continued fraction with a period of 3 is first seen (at sqrt(41)), the lowest period not yet seen is 7, which first occurs as the period of sqrt(58).

Crossrefs

Cf. A013646.

Sequence in context: A014839 A262775 A092293 * A320275 A096072 A305121

Adjacent sequences: A215482 A215483 A215484 * A215486 A215487 A215488

Keyword

nonn

Author

Patrick McKinley, Aug 12 2012

Status

approved