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A009000
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Ordered hypotenuse numbers (squares are sums of 2 distinct nonzero squares).
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18
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The largest member 'c' of the Pythagorean triples (a,b,c) ordered by increasing c.
If c^2=a^2+b^2 (a<b<c) then c^2=(n^2+m^2)/2 with n=b-a,m=b+a [From Zak Seidov Mar 03 2011]
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
| 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
| Zak Seidov and T. D. Noe, Table of n, a(n) for n = 1..10000 (Zak Seidov entered the first 1981 terms).
Anonymous, Links to Pythagorean Theorem Proofs
H. Bottomley, Pythagoras's theorem(animated proof)
Dept. of Pure Math., Univ. Sheffield, Animated Proof of Pythagoras TheoremT. 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 TheoremRon Knott, Pythagorean Triples and Online Calculators
Kangourou Math Website, L'animation du theoreme de Pythagore
R. Knott, Right-angled Triangles and Pythagoras' Theorem
I. Kobayashi et al., Pythagorean Theorem(Java Interactive Proofs, Applications and Explorations)
Mathematical Database, Poster, 7 Ways to prove the Pythagorean Theorem
B. Richmond, The Pythagorean Theorem
M. Shepperd, Web Resources on Pythagoras' Theorem
J. S. Silverman, A Friendly Introduction to Number Theory, Chap.2:Pythagorean Triples; Chap.3:Pythagorean Triples and the Unit Circle
G. Villemin's Almanach of Numbers, Triangles & Triplets de Pythagore
Eric Weisstein's World of Mathematics, Pythagorean Triple
Index entries for sequences related to sums of squares
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CROSSREFS
| Cf. A009000, A009012, A009003, A024507, A004431, A046083, A046084.
Sequence in context: A046130 A073503 A049197 * A198389 A057100 A009003
Adjacent sequences: A008997 A008998 A008999 * A009001 A009002 A009003
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KEYWORD
| nonn,nice,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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