A094136 Values x of smallest positive pair (x,y) satisfying x^2 - 2*y^2 = -+d, where d=A058529(n).

1, 1, 1, 5, 1, 3, 7, 1, 1, 9, 9, 3, 1, 5, 11, 3, 1, 5, 13, 1, 13, 3, 7, 1, 5, 15, 3, 7, 1, 17, 5, 17, 17, 1, 7, 9, 5, 3, 1, 7, 19, 19, 5, 3, 1, 7, 21, 9, 21, 21, 1, 11, 7, 23, 5, 9, 3, 1, 23, 23, 7, 5, 3, 1, 25, 7, 11, 25, 25, 5, 13, 9, 1, 7, 11, 5, 3, 9, 1, 27, 29, 7, 11, 29, 3, 1, 29, 29, 7, 29, 5

Offset

1,4

Comments

Here (x,y) is considered smaller than (u,v) iff x+y < u+v or (x+y = u+v and x < u).

Links

Table of n, a(n) for n=1..91.

Example

A058529(6) = 41; (3, 5), (7, 2), (11, 9), (13, 8), ... are pairs satisfying x^2 - 2*y^2 = -+41; (3, 5) is the smallest one, so a(6) = 3.

Prog

(PARI) {sp(d)=local(m, b, z, x, y); m=d+2; b=1; z=1; while(b&&z<m, x=1; while(b&&x<z, y=z-x; if(abs(x^2-2*y^2)==d, b=0, x++)); if(b, z++)); if(b, [ -1, -1, -1], [x, y, z])} {for(n=1, 860, fac=factor(n); v=vector(matsize(fac)[1], j, fac[j, 1])%8; b=1; for(k=1, length(v), if(v[k]>1&&v[k]<7, b=0)); if(b>0, print1(sp(n)[1], ", ")))}

Crossrefs

Cf. A058529, A094137, A094138.

Sequence in context: A053544 A174879 A327965 * A051996 A242303 A214803

Adjacent sequences: A094133 A094134 A094135 * A094137 A094138 A094139

Keyword

nonn

Author

Lekraj Beedassy, May 04 2004

Extensions

Edited, corrected and extended by Klaus Brockhaus May 31 2004

Status

approved