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Search: id:A050931
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| A050931 |
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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. |
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+0
2
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| 7, 13, 14, 19, 21, 26, 28, 31, 35, 37, 38, 39, 42, 43, 49, 52, 56, 57, 61, 62, 63, 65, 67, 70, 73, 74, 76, 77, 78, 79, 84, 86, 91, 93, 95, 97, 98, 103, 104, 105, 109, 111, 112, 114, 117, 119, 122, 124, 126, 127, 129, 130, 133, 134, 139, 140, 143, 146, 147, 148, 151
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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
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LINKS
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Planet Math, Heronian means
Eric Weisstein's World of Mathematics, Source - see especially (19)
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CROSSREFS
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Adjacent sequences: A050928 A050929 A050930 this_sequence A050932 A050933 A050934
Sequence in context: A090229 A057930 A013651 this_sequence A072864 A120100 A104217
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KEYWORD
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easy,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 30 1999
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