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A112680
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Numbers which form exclusively the shortest side of primitive Pythagorean triangles.
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1
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3, 7, 8, 9, 11, 16, 19, 20, 23, 27, 28, 31, 32, 33, 36, 39, 43, 44, 47, 48, 49, 51, 52, 57, 59, 64, 67, 68, 69, 71, 75, 76, 79, 81, 83, 87, 88, 92, 93, 95, 96, 100, 103, 104, 107, 108, 111, 115, 116, 119, 121, 123, 124, 127, 128, 129, 131, 133, 135, 136, 139, 141, 147
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OFFSET
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1,1
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COMMENTS
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Let S consist of integers x such that x is a term of a primitive Pythagorean triple (ppt). Consider the equivalence classes induced on S by this relation: x and y are equivalent if some ppt includes both x and y. For each class E, let x(E) be the least number in E. Then (a(n)) is the result of arranging the numbers x(E) in increasing order. The terms of S can be represented as nodes of a disconnected graph whose components match the classes C. For example, the component represented by a(1) = 3 starts with
. . . . . . . . . 3
. . . . . . . . / ... \
. . . . . . . 4 ------- 5
. . . . . . . . . . . /...\
. . . . . . . . . . 12 -----13
. . . . . . . . . ./...\ .. /..\
. . . . . . . . . 35---37..84--85
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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