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

1,1

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.

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A058340 A138537 A271983 * A054723 A109981 A091367

Adjacent sequences: A135997 A135998 A135999 * A136001 A136002 A136003

Keyword

nonn,easy

Author

Omar E. Pol, Dec 10 2007

Extensions

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

Extended by Ray Chandler, Dec 13 2008

Status

approved