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Search: id:A009000
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| A009000 |
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Ordered hypotenuse numbers (squares are sums of 2 distinct nonzero squares). |
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16
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| 5, 10, 13, 15, 17, 20, 25, 25, 26, 29, 30, 34, 35, 37, 39, 40, 41, 45, 50, 50, 51, 52, 53, 55, 58, 60, 61, 65, 65, 65, 65, 68, 70, 73, 74, 75, 75, 78, 80, 82, 85, 85, 85, 85, 87, 89, 90, 91, 95, 97, 100, 100, 101, 102, 104, 105, 106, 109, 110, 111, 113, 115, 116, 117, 119, 120
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The largest member 'c' of the Pythagorean triples (a,b,c) ordered by increasing c.
Numbers n such that A083025(n)>0, i.e., n is divisible by at least one prime of the form 4k+1. [From Max Alekseyev (maxale(AT)gmail.com), Oct 24 2008]
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REFERENCES
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W. L. Schaaf, Recreational Mathematics, A Guide To The Literature, "The Pythagorean Relationship", Chapter 6 pp. 89-99 NCTM VA 1963.
W. L. Schaaf, A Bibliography of Recreational Mathematics, Vol. 2, "The Pythagorean Relation", Chapter 6 pp. 108-113 NCTM VA 1972.
W. L. Schaaf, A Bibliography of Recreational Mathematics, Vol. 3, "Pythagorean Recreations", Chapter 6 pp. 62-6 NCTM VA 1973.
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LINKS
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Ron Knott, Pythagorean Triples and Online Calculators
Eric Weisstein's World of Mathematics, Pythagorean Triple
Index entries for sequences related to sums of squares
R. Knott, Right-angled Triangles and Pythagoras' Theorem
Anonymous, Links to Pythagorean Theorem Proofs
I. Kobayashi et al., Pythagorean Theorem(Java Interactive Proofs, Applications and Explorations)
G. Villemin's Almanach of Numbers, Triangles & Triplets de Pythagore
Dept. of Pure Math., Univ. Sheffield, Animated Proof of Pythagoras Theorem
M. Shepperd, Web Resources on Pythagoras' Theorem
B. Richmond, The Pythagorean Theorem
Mathematical Database, Poster, 7 Ways to prove the Pythagorean Theorem
Kangourou Math Website, L'animation du theoreme de Pythagore
H. Bottomley, Pythagoras's theorem(animated proof)
J. S. Silverman, A Friendly Introduction to Number Theory, Chap.2:Pythagorean Triples; Chap.3:Pythagorean Triples and the Unit Circle
T. Eveilleau, Animated proofs of the Pythagorean theorem:Sample Ancient Proofs(Text in French)
T. Eveilleau, More Animated proofs of the Pythagorean theorem (Text in French)
T. Eveilleau, An Experimental Illustration of the Pythagorean Theorem
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CROSSREFS
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Cf. A009000, A009012, A009003, A024507, A004431, A046083, A046084.
Sequence in context: A046130 A073503 A049197 this_sequence A057100 A009003 A071821
Adjacent sequences: A008997 A008998 A008999 this_sequence A009001 A009002 A009003
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KEYWORD
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nonn,nice,easy
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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