A259684 Let m = A062695(n); a(n) is value of a in decomposition of m defined in Comments.

3, 5, 3, 5, 2, 1, 3, 4, 1, 1, 1, 9, 153, 7, 7, 6, 13, 5, 1, 17, 1, 11, 4, 1, 4, 4, 11, 253, 4, 1, 1, 1, 1, 5, 5, 2, 8, 1, 1, 4, 103, 39, 29, 2, 5, 19, 8, 7, 1, 1, 163, 4, 8, 63, 44, 23, 35, 7, 2, 5, 4, 5, 13, 17, 1, 12, 5, 8, 193, 22, 25, 65, 29, 481, 1, 85, 1

Offset

1,1

Comments

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

Links

Table of n, a(n) for n=1..77.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Crossrefs

Cf. A003273, A006991, A062695, A259680-A259687.

Sequence in context: A254327 A175999 A236965 * A214287 A010703 A107489

Adjacent sequences: A259681 A259682 A259683 * A259685 A259686 A259687

Keyword

nonn

Author

N. J. A. Sloane, Jul 04 2015

Extensions

More terms from Jinyuan Wang, Jan 01 2021

Status

approved