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

1,1

Links

Table of n, a(n) for n=1..33.

Prog

(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))); }

Crossrefs

Cf. A086378 and A088900.

Sequence in context: A050209 A109142 A014576 * A184369 A073938 A278285

Adjacent sequences: A087411 A087412 A087413 * A087415 A087416 A087417

Keyword

nonn

Author

Thomas Baruchel, Oct 21 2003

Status

approved