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A106505
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Ordered and uniqued length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.
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5
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5, 7, 9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 25, 27, 29, 31, 32, 33, 35, 37, 39, 40, 41, 43, 45, 47, 48, 49, 51, 53, 55, 56, 57, 59, 61, 63, 64, 65, 67, 69, 71, 72, 73, 75, 77, 79, 80, 81, 83, 85, 87, 88, 89, 91, 93, 95, 96, 97, 99, 101, 103, 104, 105, 107, 109, 111, 112
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OFFSET
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1,1
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COMMENTS
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The terms are proposed without repetition. For example, there exist two such triangles with a length of side = 33. They correspond respectively to s^2 - r^2 = 33 (see formula) with (r, s) = (4, 7) and sides (33, 28, 16), and the other triangle with (r, s) = (16, 17) and sides (33, 272, 256). Lengths = 39, 51, 57, 69, 75, ... correspond to two distinct triangles ... The lengths of these sides are proposed with repetition in A343064. - Bernard Schott, Apr 22 2021
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LINKS
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Table of n, a(n) for n=1..67.
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FORMULA
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Values s^2 - r^2, where r<s<2r and (r, s)=1.
Conjecture: for n>2, a(n+5) = a(n) + 8. - Ralf Stephan, Nov 16 2010.
Empirical g.f.: -x*(x^7+x^6+3*x^5-2*x^4-2*x^3-2*x^2-2*x-5) / ((x-1)^2*(x^4+x^3+x^2+x+1)). - Colin Barker, Oct 05 2013
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CROSSREFS
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Cf. A106499-A106506, A106410, A106420, A106430, A321499.
Cf. A343063, A343064, A343065, A343066, A343067.
Sequence in context: A177088 A168146 A343064 * A097985 A342378 A099047
Adjacent sequences: A106502 A106503 A106504 * A106506 A106507 A106508
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy, May 04 2005
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EXTENSIONS
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Extended by Ray Chandler, May 09 2005
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STATUS
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approved
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