A240071 - OEIS

%I #11 Oct 25 2014 14:42:58

%S 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,

%T 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,

%U 2,4,2,1,8,4,1,3,1,8,4,1,8,5,5,10,5,5,10

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

%H T. D. Noe, <a href="/A240071/b240071.txt">Rows n = 1..1000 of irregular triangle, flattened</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/SimpleContinuedFraction.html">Simple continued fraction</a>

%e Irregular table in which the first term is the non-repeating part:

%e {1},

%e {1, 2},

%e {1, 1, 2},

%e {2},

%e {2, 4},

%e {2, 2, 4},

%e {2, 1, 1, 1, 4},

%e {2, 1, 4},

%e {3},

%e {3, 6},

%e {3, 3, 6},

%e {3, 2, 6},

%e {3, 1, 1, 1, 1, 6},

%e {3, 1, 2, 1, 6}

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

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

%K nonn,tabf

%O 1,3

%A _T. D. Noe_, Apr 04 2014