%I #8 Oct 10 2017 22:00:22
%S 153,1717,2244,2340,3525,3650,6460,7119,7475,10074,14490,19147,20008,
%T 20862,21424,21747,24453,25400,26039,27346,28028,28371,31484,35483,
%U 37008,44275,44678,45974,50389,52155,62187,63724,64752
%N Numbers n such that 2*n*k(n) is rational but not an integer, where k(n) is sum of successive remainders when computing the Euclidean algorithm for (1, 1/sqrt(n)) as defined in A086378 (MuPAD program is given there); numbers belonging to A086378 but not to A088900.
%o (PARI) /* z(n)!=0 iff n is in the sequence */
%o z(n)= { local(a,b,c,d,e,f,g,h,i,j,k);
%o b=a=sqrtint(n);d=f=i=1;e=g=h=0;j=c=n-a^2;if(!c,return(0));
%o until((a==b)&&(c==j),k=d+a*e;f*=c;d=a*d+e*n;e=k;g+=i;i*=c;
%o k=g+a*h;g=a*g+h*n;h=k;k=(a+b)\c;g-=i*k;a=c*k-a;c=(n-a^2)/c);
%o d=d/f-1;e/=f;g/=i;h/=i;i=d^2-n*e^2;k=h*d-g*e;g=g*d-h*e*n;
%o b=n-a^2;a=b*g-c*a*i;c=b*k+i*c;b*=i;!a*(2%(b/gcd(b,n*c))); }
%Y Cf. A086378 and A088900.
%K nonn
%O 1,1
%A _Thomas Baruchel_, Oct 21 2003