A215485 Periods of square root continued fractions at which A013646 sets a new record.

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, 1775, 1781, 1951, 2011

Offset: 0

Author

Patrick McKinley, Aug 12 2012

Keywords

• nonn

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?

Examples

			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).
		

Links

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

Crossrefs

Cf. A013646.