A087414 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.
153, 1717, 2244, 2340, 3525, 3650, 6460, 7119, 7475, 10074, 14490, 19147, 20008, 20862, 21424, 21747, 24453, 25400, 26039, 27346, 28028, 28371, 31484, 35483, 37008, 44275, 44678, 45974, 50389, 52155, 62187, 63724, 64752
Offset: 1
Keywords
Programs
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PARI
/* z(n)!=0 iff n is in the sequence */ z(n)= { local(a,b,c,d,e,f,g,h,i,j,k); b=a=sqrtint(n);d=f=i=1;e=g=h=0;j=c=n-a^2;if(!c,return(0)); until((a==b)&&(c==j),k=d+a*e;f*=c;d=a*d+e*n;e=k;g+=i;i*=c; 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); 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; b=n-a^2;a=b*g-c*a*i;c=b*k+i*c;b*=i;!a*(2%(b/gcd(b,n*c))); }
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