Search: id:A087642
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%I A087642
%S A087642 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 A087642 59,62,66,67,69,70,71,77,78,79,83,86,87,91,93,94,95,102,103,105,107,110,
%U A087642 111,114,115,118,119,123,127,129,131,133,134,138,139,141,142,143,146
%N A087642 Sequence of square-free n such that Q(sqrt(n)) has no element with a 
               fully periodical continued fraction of period 1.
%C A087642 Diophantine equation x^2 - n.y^2 + 4 = 0 has no solution (x,y) for a 
               given square-free n. Square-free n not in the sequence A013946. Same 
               sequence with square factors allowed is A087643.
%e A087642 3 is in the sequence because no [k,k,k,k,...] is in Q(sqrt(3))
%e A087642 5 is not in the sequence since Q(sqrt(5)) contains [1,1,1,1,...]
%Y A087642 Cf. A087643, A013946.
%Y A087642 Sequence in context: A022550 A153033 A076644 this_sequence A084349 A126003 
               A047556
%Y A087642 Adjacent sequences: A087639 A087640 A087641 this_sequence A087643 A087644 
               A087645
%K A087642 easy,nonn
%O A087642 3,1
%A A087642 Thomas Baruchel (baruchel(AT)users.sourceforge.net), Sep 16 2003

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