A165564 Numbers which are not congruent numbers, i.e., positive integers which are not the area of any right triangle with rational sides.

1, 2, 3, 4, 8, 9, 10, 11, 12, 16, 17, 18, 19, 25, 26, 27, 32, 33, 35, 36, 40, 42, 43, 44, 48, 49, 50, 51, 57, 58, 59, 64, 66, 67, 68, 72, 73, 74, 75, 76, 81, 82, 83, 89, 90, 91, 97, 98, 99, 100, 104, 105, 106, 107, 108, 113, 114, 115, 121, 122, 123, 128, 129, 130

Offset

1,2

Comments

It is known that every positive integer is the area of some triangle with rational sides. See the survey by Top and Yui. - Jonathan Sondow, Nov 15 2017

References

Alter, Ronald; Curtz, Thaddeus B.; Kubota, K. K. Remarks and results on congruent numbers. Proceedings of the Third Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1972), pp. 27-35. Florida Atlantic Univ., Boca Raton, Fla., 1972. MR0349554 (50 #2047). - From N. J. A. Sloane, Apr 28 2012

Links

Michel Marcus, Table of n, a(n) for n = 1..4258

Boris Iskra, Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8, Proc. Japan Acad. Ser. A Math. Sci., Volume 72, Number 7 (1996), 168-169.

J. Top and N. Yui, Congruent number problems and their variants, Mathematical Sciences Research Institute Publications, 44 (2008), 613-639.

Formula

Integers \ { A003273 }.

Crossrefs

Complement of A003273.

Sequence in context: A370662 A047453 A037467 * A326704 A309314 A309326

Adjacent sequences: A165561 A165562 A165563 * A165565 A165566 A165567

Keyword

nonn

Author

Jose Brox (brox(AT)agt.cie.uma.es), Sep 22 2009

Extensions

Name corrected by Jonathan Sondow, Nov 15 2017

Status

approved