A240071 Irregular triangle of the simple continued fraction of sqrt(n).

1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 4, 2, 1, 1, 1, 4, 2, 1, 4, 3, 3, 6, 3, 3, 6, 3, 2, 6, 3, 1, 1, 1, 1, 6, 3, 1, 2, 1, 6, 3, 1, 6, 4, 4, 8, 4, 4, 8, 4, 2, 1, 3, 1, 2, 8, 4, 2, 8, 4, 1, 1, 2, 1, 1, 8, 4, 1, 2, 4, 2, 1, 8, 4, 1, 3, 1, 8, 4, 1, 8, 5, 5, 10, 5, 5, 10

Offset: 1

Author

T. D. Noe, Apr 04 2014

Keywords

• nonn
• tabf

Examples

			Irregular table in which the first term is the non-repeating part:
{1},
{1, 2},
{1, 1, 2},
{2},
{2, 4},
{2, 2, 4},
{2, 1, 1, 1, 4},
{2, 1, 4},
{3},
{3, 6},
{3, 3, 6},
{3, 2, 6},
{3, 1, 1, 1, 1, 6},
{3, 1, 2, 1, 6}
		

Links

• T. D. Noe, Rows n = 1..1000 of irregular triangle, flattened
• Eric W. Weisstein, Simple continued fraction

Crossrefs

Cf. A067280 (length of the continued fraction of sqrt(n)).

Programs

Mathematica

Table[Flatten[ContinuedFraction[Sqrt[n]]], {n, 30}]