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Search: id:A053630
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| A053630 |
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Pythagorean spiral: a(n-1), a(n)-1 and a(n) are sides of a right angled triangle. |
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+0
2
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| 3, 5, 13, 85, 3613, 6526885, 21300113901613, 226847426110843688722000885, 25729877366557343481074291996721923093306518970391613
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(3)=85 because 13,84,85 is a Pythagorean triple and a(2)=13
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FORMULA
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a(n) = (a(n-1)^2+1)/2
a(n) =2*A000058(n)-1 =A053631(n)+1 =floor[2 * 1.597910218031873...^(2^n)]. Constructing the spiral as a sequence of triangles with one vertex at the origin, then for large n the other vertices are close to lying on the doubly logarithmic spiral r=2*2.228918357655...^(1.5546822754821...^theta) where theta(n)=n*pi/2-1.215918200344... and 1.5546822754821...=4^(1/pi).
a(1) = 3, a(n+1) = (1/4)[{a(n)-1}^2 + {a(n)+1}^2] - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 17 2005
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CROSSREFS
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Cf. A001844.
Sequence in context: A159293 A051901 A018928 this_sequence A155012 A121533 A087170
Adjacent sequences: A053627 A053628 A053629 this_sequence A053631 A053632 A053633
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 21 2000
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EXTENSIONS
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Corrected and extended by James A. Sellers (sellersj(AT)math.psu.edu), Mar 22 2000.
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