A136000 a(n) = A010814(n) - 1.

11, 23, 29, 35, 39, 47, 55, 59, 69, 71, 79, 83, 89, 95, 107, 111, 119, 125, 131, 139, 143, 149, 153, 155, 159, 167, 175, 179, 181, 191, 197, 199, 203, 207, 209, 215, 219, 223, 227, 233, 239, 251, 259, 263, 269, 275, 279, 285, 287, 299, 305, 307, 311, 319, 323

Offset: 1

Author

Omar E. Pol, Dec 10 2007

Keywords

• nonn
• easy

Comments

Numbers of the form P-1 in increasing order, where P is the sum of a Pythagorean triple. Also P is the perimeter of a Pythagorean triangle. The open triangle represent a triangle instrument and, in general, any musical instrument. Positive integers are musician numbers or dancer number A136002.

Examples

			a(1) = 11 because {3,4,5} is a Pythagorean triple and 3+4+5 = 12 is the sum of a Pythagorean triple and 11+1 = 12, then we can write 3+4+5 = 11+1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Dallas Symphony Association, Dsokids - Triangle instrument.
• Epsilones, Pythagoras - Music.
• Ron Knott, Pythagorean Triples and Online Calculators.

Crossrefs

Cf. A010814, A136001, A136002, A009096 (perimeters of Pythagorean triangles).

Programs

Mathematica

q[n_] := OddQ[n] && Module[{d = Divisors[(n+1)/2]}, AnyTrue[Range[3, Length[d]], d[[#]] < 2 * d[[#-1]] &]]; Select[Range[350], q] (* Amiram Eldar, Oct 19 2024 *)

Extensions

Definition corrected by R. J. Mathar, Dec 12 2007

Extended by Ray Chandler, Dec 13 2008