cp's OEIS Frontend

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

%I A136000 #16 Oct 20 2024 03:35:24
%S A136000 11,23,29,35,39,47,55,59,69,71,79,83,89,95,107,111,119,125,131,139,
%T A136000 143,149,153,155,159,167,175,179,181,191,197,199,203,207,209,215,219,
%U A136000 223,227,233,239,251,259,263,269,275,279,285,287,299,305,307,311,319,323
%N A136000 a(n) = A010814(n) - 1.
%C A136000 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.
%H A136000 Amiram Eldar, <a href="/A136000/b136000.txt">Table of n, a(n) for n = 1..10000</a>
%H A136000 Dallas Symphony Association, <a href="https://www.dallassymphony.org/community-education/dso-kids/listen-watch/instruments/triangle/">Dsokids - Triangle instrument</a>.
%H A136000 Epsilones, <a href="https://web.archive.org/web/20160303215728/https://www.epsilones.com/imagenes/historia/pitagoras-musica.gif">Pythagoras - Music</a>.
%H A136000 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A136000 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.
%t A136000 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 *)
%Y A136000 Cf. A010814, A136001, A136002, A009096 (perimeters of Pythagorean triangles).
%K A136000 nonn,easy
%O A136000 1,1
%A A136000 _Omar E. Pol_, Dec 10 2007
%E A136000 Definition corrected by _R. J. Mathar_, Dec 12 2007
%E A136000 Extended by _Ray Chandler_, Dec 13 2008