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

1,1

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

Links

Table of n, a(n) for n=1..67.

Formula

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

Crossrefs

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

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

Sequence in context: A362486 A168146 A343064 * A097985 A362570 A342378

Adjacent sequences: A106502 A106503 A106504 * A106506 A106507 A106508

Keyword

nonn

Author

Lekraj Beedassy, May 04 2005

Extensions

Extended by Ray Chandler, May 09 2005

Status

approved