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Search: id:A009177
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| A009177 |
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Hypotenuses of more than one Pythagorean triangle. |
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5
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| 25, 50, 65, 75, 85, 100, 125, 130, 145, 150, 169, 170, 175, 185, 195, 200, 205, 221, 225, 250, 255, 260, 265, 275, 289, 290, 300, 305, 325, 338, 340, 350, 365, 370, 375, 377, 390, 400, 410, 425, 435, 442, 445, 450, 455, 475, 481, 485, 493, 500, 505, 507, 510, 520, 525
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also, hypotenuses of pythagorean triangle in pythagorean triples (a,b,c, a<b<c) such that a and b are the hypotenuse of pythagorean triangle, where the pythagorean triples (x1,y1,a) and (x2,y2,b) are similar triangle. sequence gives c values. -Naohiro Nomoto
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LINKS
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Index entries for sequences related to sums of squares
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FORMULA
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Of the form b(i)*b(j)*k, where b(n) is A004431(n). Numbers whose prime factorization includes at least 2 (not necessarily distinct) primes congruent to 1 mod 4. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006. [Typo corrected by Ant King, Jul 17 2008]
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EXAMPLE
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25^2 = 24^2+7^2 = 20^2+15^2.
e.g. (a=15, b=20, c=25, a^2+b^2=c^2) ; 15 and 20 are the hypotenuse of pythagorean triangle. The pythagorean triples (9, 12, 15) and (12, 16, 20) are similar triangle. So c=25 is in the sequence. -Naohiro Nomoto
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MATHEMATICA
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Clear[lst, f, n, i, k] f[n_]:=Module[{i=0, k=0}, Do[If[Sqrt[n^2-i^2]==IntegerPart[Sqrt[n^2-i^2]], k++ ], {i, n-1, 1, -1}]; k]; lst={}; Do[If[f[n]>2, AppendTo[lst, n]], {n, 4*5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 12 2009]
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CROSSREFS
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Cf. A004431, A118882.
Sequence in context: A076637 A040600 A033902 this_sequence A118882 A085625 A116490
Adjacent sequences: A009174 A009175 A009176 this_sequence A009178 A009179 A009180
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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