A136001 -id:A136001 - cp's OEIS frontend

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

Omar E. Pol, Dec 10 2007

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.

			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.

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.

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

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 *)

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

Extended by Ray Chandler, Dec 13 2008

cp's OEIS Frontend

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

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