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Search: id:A058529
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| A058529 |
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Numbers whose prime factors are +-1 mod 8. |
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+0
22
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| 1, 7, 17, 23, 31, 41, 47, 49, 71, 73, 79, 89, 97, 103, 113, 119, 127, 137, 151, 161, 167, 191, 193, 199, 217, 223, 233, 239, 241, 257, 263, 271, 281, 287, 289, 311, 313, 329, 337, 343, 353, 359, 367, 383, 391, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values B-A, sorted; terms > 1 in sequence give values of A + B, sorted. Ordered set of (semiperimeter + radius of largest inscribed circle) of all primitive Pythagorean triangles.
Semiperimeter + radius of largest inscribed circle = ((a+b+c)/2) + ((a+b-c)/2) = a + b (I cannot explain this).
a(n+1) in Frenicle page 31: Methode pour trouver .., 44 pages.In Divers ouvrages de mathematique .. Par Messieurs de l'Academie Royale des Sciences,in-fol,6+518+1PP,Paris,1693. [From Paul Curtz (bpcrtz(AT)free.fr), Sep 06 2008]
The terms of this sequence appear to be of the form 6N+/-1, as indeed are prime numbers [From J.T.Harrison (harrison_uk_2000(AT)yahoo.co.uk), Apr 28 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
K. S. Brown, Pythagorean graphs
F. Barnes, primitive Pythagorean triangles where a-b is a constant
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FORMULA
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a(n) = A046086(n) + A046087(n) Is similar to A001132, but includes composites whose factors are in A001132. Can be generated in this manner. (a + b) for all primitive Pythagorean triples (a, b, c), sorted.
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CROSSREFS
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Cf. A020882-A020886, A020888, A046086, A046087, A014498, A001132.
Cf. A001653.
Sequence in context: A087168 A032454 A107643 this_sequence A120681 A001132 A165353
Adjacent sequences: A058526 A058527 A058528 this_sequence A058530 A058531 A058532
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KEYWORD
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easy,nice,nonn
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AUTHOR
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William Bagby (bagsbee(AT)aol.com), Dec 24 2000
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EXTENSIONS
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More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 02 2001
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