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A136000
a(n) = A010814(n) - 1.
3
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.
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
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