A003273 -id:A003273 - cp's OEIS frontend

A259686 Let m = A062695(n); a(n) is value of c in decomposition of m defined in Comments.

1, 3, 1, 17, 1, 3, 1, 3, 5, 1, 5, 7, 7, 3, 1, 1, 5, 11, 1, 15, 5, 7, 1, 1, 1, 1, 1, 7, 1, 9, 15, 1, 1, 1, 1, 5, 9, 7, 17, 1, 97, 7, 799, 11, 49, 17, 1, 3, 1, 1, 63, 1, 1, 55, 161, 3, 1, 1, 1, 1, 1, 161, 7, 1, 1, 1, 1, 7, 3783, 1, 7, 1697, 21, 319, 21, 911, 3, 1

Offset: 1

N. J. A. Sloane, Jul 04 2015

nonn

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.

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]

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

More terms from Jinyuan Wang, Jan 01 2021

A337704 Pythagorean primes that are not congruent numbers.

Original entry on oeis.org

17, 73, 89, 97, 113, 193, 233, 241, 281, 337, 401, 409, 433, 449, 521, 569, 577, 593, 601, 617, 641, 673, 769, 809, 857, 881, 929, 937, 953, 977, 1009, 1033, 1049, 1097, 1129, 1153, 1193, 1289, 1297, 1361, 1409, 1433, 1481, 1489, 1553, 1601, 1609, 1657, 1697, 1721, 1753

Offset: 1

Jani Melik, Sep 16 2020

nonn

			17 is a Pythagorean prime and is not congruent because it is not the area of a right triangle with rational sides. So 17 is a term.

Intersection of A002144 and A165564.

Cf. A003273, A269727, A165815.

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A259686 Let m = A062695(n); a(n) is value of c in decomposition of m defined in Comments.

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A337704 Pythagorean primes that are not congruent numbers.

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