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Search: id:A114336
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| A114336 |
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Pythagorean triples of nearly isosceles triangle. |
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+0
2
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| 3, 4, 5, 20, 21, 29, 119, 120, 169, 696, 697, 985, 4059, 4060, 5741, 23660, 23661, 33461, 137903, 137904, 195025
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Pythagorean triples of exact isosceles triangles do not exist because 2a^2 = c^2 has no integer solution. a^2 + (a+1)^2 = c^2 are nearly isosceles triangles and give a recursive serie.
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FORMULA
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a^2 + (a+1)^2 = c^2 a(n) = 3a(n-1) + 2c(n-1) + 1 c(n) = 4a(n-1) + 3c(n-1) + 2
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EXAMPLE
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119^2 + 120^2 = 169^2
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PROGRAM
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a(1):= 3 c(1):= 5 read m C m is infinite but limited by integer overflow of c(n) for n:=2 until m step 1 a(n):= 3*a(n-1) + 2*c(n-1) + 1 c(n):= 4*a(n-1) + 3*c(n-1) + 2 print a(n), a(n)+1, c(n) next n end
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CROSSREFS
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Sequence in context: A031199 A059184 A084930 this_sequence A048086 A048005 A039573
Adjacent sequences: A114333 A114334 A114335 this_sequence A114337 A114338 A114339
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Heinrich Baldauf (heinbald25(AT)web.de), Feb 07 2006
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