Search: id:A050931
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%I A050931
%S A050931 7,13,14,19,21,26,28,31,35,37,38,39,42,43,49,52,56,57,61,62,63,65,67,
%T A050931 70,73,74,76,77,78,79,84,86,91,93,95,97,98,103,104,105,109,111,112,114,
%U A050931 117,119,122,124,126,127,129,130,133,134,139,140,143,146,147,148,151
%N A050931 Solutions c of cot(2*Pi/3)*(-(a+b+c)*(-a+b+c)*(-a+b-c)*(a+b-c))^(1/2)=a^2+b^2-c^2, 
               c>a,b integers.
%C A050931 Also the c-values for solutions to c^2 = a^2 + ab + b^2 in positive integers. 
               Also the numbers which occur as the longest side of some triangle 
               with integer sides and a 120 degree angle. - Paul Boddington (pbotherstuff(AT)yahoo.co.uk), 
               Nov 05 2007
%C A050931 The sequence can also be defined as the numbers w which are Heronian 
               means of two distinct positive integers u and v, i.e. w = [u+sqrt(uv)+v]/
               3. E.g. 28 is the Heronian mean of 4 and 64 (and also of 12 and 48). 
               - Pahikkala Jussi (pahio(AT)uusikaupunki.fi), Feb 16 2008
%H A050931 Planet Math, <a href="http://planetmath.org/encyclopedia/TruncatedCone.html">
               Heronian means</a>
%H A050931 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Triangle.html">Source - see especially (19)</a>
%Y A050931 Sequence in context: A090229 A057930 A013651 this_sequence A072864 A120100 
               A104217
%Y A050931 Adjacent sequences: A050928 A050929 A050930 this_sequence A050932 A050933 
               A050934
%K A050931 easy,nonn
%O A050931 1,1
%A A050931 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 30 1999

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