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Search: id:A137515
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| A137515 |
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Maximal number of right-angled triangles in n turns of the Pythagoras's snail. |
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+0
1
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| 16, 53, 109, 185, 280, 395, 531, 685, 860, 1054, 1268, 1502, 1756, 2029, 2322, 2635, 2967, 3319, 3691, 4083, 4494, 4926, 5376, 5847, 6337, 6848, 7377, 7927, 8496, 9086, 9694, 10323, 10971, 11639, 12327, 13035, 13762, 14509, 15276, 16062, 16868, 17694
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Pythagoras's snail : begin the snail with an isosceles triangle (side = 1 unit). Then new triangle's right-angle sides are the previous hypotenuse and 1 unit length side.
From one term to the next one, the number added grows by 18, 19, 20 or 21 (tested up to 5000 terms).
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EXAMPLE
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17 triangles are needed to close the first turn. So there are 16 triangles in this turn. From the beginning, there are 53 triangles before closing the second turn... etc.
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PROGRAM
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(PYTHON) from math import asin, sqrt, pi hyp=2 som=0 n=1 while n<500: if som+asin(1/sqrt(hyp))/pi*180>n*360: print hyp-2 n=n+1 som=som+asin(1/sqrt(hyp))/pi*180 hyp=hyp+1
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CROSSREFS
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Sequence in context: A087701 A087973 A117273 this_sequence A137741 A122658 A029719
Adjacent sequences: A137512 A137513 A137514 this_sequence A137516 A137517 A137518
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Apr 23 2008, Apr 25 2008
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