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

1,3

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.

Links

T. D. Noe, Rows n = 1..1000 of irregular triangle, flattened

Eric W. Weisstein, Simple continued fraction

Example

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}
  ...

Mathematica

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

Crossrefs

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

Sequence in context: A117942 A290092 A066877 * A029255 A029272 A153904

Adjacent sequences: A240068 A240069 A240070 * A240072 A240073 A240074

Keyword

nonn,tabf

Author

T. D. Noe, Apr 04 2014

Status

approved