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

Author

Thomas Baruchel, Oct 21 2003

Keywords

• nonn

Crossrefs

Cf. A086378 and A088900.

Programs

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))); }