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
KEYWORD
nonn,easy,changed
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