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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 12:24 EST 2023. Contains 359840 sequences. (Running on oeis4.)