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Sequence of squarefree n such that Q(sqrt(n)) has no element with a fully periodical continued fraction of period 1.
1

%I #5 Nov 02 2014 18:39:41

%S 3,6,7,11,14,15,19,21,22,23,30,31,33,34,35,38,39,42,43,46,47,51,55,57,

%T 59,62,66,67,69,70,71,77,78,79,83,86,87,91,93,94,95,102,103,105,107,

%U 110,111,114,115,118,119,123,127,129,131,133,134,138,139,141,142,143,146

%N Sequence of squarefree n such that Q(sqrt(n)) has no element with a fully periodical continued fraction of period 1.

%C Diophantine equation x^2 - n.y^2 + 4 = 0 has no solution (x,y) for a given squarefree n. Squarefree n not in the sequence A013946. Same sequence with square factors allowed is A087643.

%e 3 is in the sequence because no [k,k,k,k,...] is in Q(sqrt(3))

%e 5 is not in the sequence since Q(sqrt(5)) contains [1,1,1,1,...]

%Y Cf. A087643, A013946.

%K easy,nonn

%O 3,1

%A _Thomas Baruchel_, Sep 16 2003