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Least positive integer multiples of angle x such that their direction cosines form a unit vector: sum(k>0, cos(a(k)*x)^2)=1, where a(1)=1 and x=1.
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%I #12 Feb 29 2020 06:45:30

%S 1,2,4,5,8,11,33,55,77,99,121,322,344,366,388,699,39394,49689,51109,

%T 51819,52174,52529,156167,156522,260515,364508,364863,573204,885893,

%U 1406923,1719612,4846147,5992555,10265498,11411906,15684849,21104200

%N Least positive integer multiples of angle x such that their direction cosines form a unit vector: sum(k>0, cos(a(k)*x)^2)=1, where a(1)=1 and x=1.

%H Hugo Pfoertner, <a href="/A080136/b080136.txt">Table of n, a(n) for n = 1..66</a>

%o (PARI) x=1; z=cos(x)^2; a=1; for(n=1,45,b=a+1; while(z+cos(b*x)^2>1,b++); z=z+cos(b*x)^2; a=b; print1(b,","))

%Y Cf. A080137, A080138, A080139, A080140.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jan 30 2003

%E Extended with PARI program by _Benoit Cloitre_, Feb 04 2003