A106505 Ordered and uniqued length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.

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

Offset: 1

Author

Lekraj Beedassy, May 04 2005

Keywords

• nonn

Comments

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

Crossrefs

Cf. A106499-A106506, A106410, A106420, A106430, A321499.

Cf. A343063, A343064, A343065, A343066, A343067.

Formula

Values s^2 - r^2, where r

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

Extensions

Extended by Ray Chandler, May 09 2005

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