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Search: id:A077034
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| A077034 |
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a(1)=3; a(n), a(n+1) are smallest > a(n-1) such that a(n-1)^2+a(n)^2=a(n+1)^2. |
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2
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| 3, 4, 5, 12, 13, 84, 85, 132, 157, 12324, 12325, 15960, 20165, 26280, 33125, 79500, 86125, 95400, 128525, 152040, 199085
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that each time two more terms are added simultaneously. The sequence is infinite.
Smallest sequence of Pythagorean triples {a(k-1),a(k),a(k+1)},with k=2n,such that the hypotenuse of one triangle is the short leg of the next one. Such a sequence is called 2-prime Pythagorean because only the first two triangles (3,4,5),(5,12,13) both have prime hypotenuse and short leg. The next such sequence is given by A076604. Actually, the starting terms for all 2-prime and 3-prime Pythagorean triangles are given respectively by A048270 and A048295. The starting term for the smallest n-prime Pythagorean triangle is A105318. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 16 2005
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EXAMPLE
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a(1)=3 therefore a(2)=4 and a(3)=5: 3^2+4^2=5^2; a(3)=5 therefore a(4)=12 and a(5)=13: 5^2+12^2=13^2.
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CROSSREFS
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Cf. A068340, A076542, A077030-A077033.
Sequence in context: A046964 A055493 A109350 this_sequence A076601 A090829 A141290
Adjacent sequences: A077031 A077032 A077033 this_sequence A077035 A077036 A077037
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Oct 21 2002
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