A031175 Shortest edge c of (measured by the longest edge) primitive Euler bricks (a, b, c, sqrt(a^2 + b^2), sqrt(b^2 + c^2), sqrt(a^2 + c^2) are integers).

44, 240, 140, 85, 160, 1008, 187, 429, 832, 780, 828, 1560, 528, 195, 1155, 1755, 495, 1575, 2964, 7840, 2925, 1008, 4368, 1080, 10296, 7579, 8789, 6072, 14112, 5643, 4599, 4900, 6435, 935, 7920, 7800, 4928, 7560, 23760, 1105, 2163, 2964

Offset

1,1

Comments

Primitive means that gcd(a,b,c) = 1.

See A031173 for a list of the 3356 primitive bricks with c < b < a < 5*10^8. - Giovanni Resta, Mar 23 2014

References

Calculated by F. Helenius (fredh(AT)ix.netcom.com).

Links

Giovanni Resta, Table of n, a(n) for n = 1..3556

R. R. Gallyamov, I. R. Kadyrov, D. D. Kashelevskiy, A fast modulo primes algorithm for searching perfect cuboids and its implementation, arXiv preprint arXiv:1601.00636 [math.NT], 2016.

A. A. Masharov and R. A. Sharipov, A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture, arXiv preprint, 2015.

J. Ramsden and H. Sharipov, Inverse problems associated with perfect cuboids, arXiv preprint arXiv:1207.6764, 2012. - From N. J. A. Sloane, Dec 23 2012

J. Ramsden and H. Sharipov, On singularities of the inverse problems associated with perfect cuboids, arXiv preprint arXiv:1208.1859, 2012. - From N. J. A. Sloane, Dec 25 2012

Ruslan Sharipov, Perfect cuboids and irreducible polynomials, arXiv:1108.5348, 2011

Ruslan Sharipov, A note on the first cuboid conjecture, arXiv:1109.2534, 2011

Ruslan Sharipov, A note on the second cuboid conjecture. Part I, arXiv:1201.1229, 2012

Ruslan Sharipov, Perfect cuboids and multisymmetric polynomials, arXiv preprint arXiv:1205.3135, 2012. - From N. J. A. Sloane, Oct 22 2012

Ruslan Sharipov, On an ideal of multisymmetric polynomials associated with perfect cuboids, arXiv preprint arXiv:1206.6769, 2012. - From N. J. A. Sloane, Dec 17 2012

Ruslan Sharipov, On the equivalence of cuboid equations and their factor equations, arXiv preprint arXiv:1207.2102, 2012. - From N. J. A. Sloane, Dec 22 2012

Ruslan Sharipov, A biquadratic Diophantine equation associated with perfect cuboids, arXiv preprint arXiv:1207.4081, 2012. - From N. J. A. Sloane, Dec 23 2012

Ruslan Sharipov, On a pair of cubic equations associated with perfect cuboids, arXiv preprint arXiv:1208.0308, 2012. - From N. J. A. Sloane, Dec 23 2012

Ruslan Sharipov, On two elliptic curves associated with perfect cuboids, arXiv preprint arXiv:1208.1227, 2012. - From N. J. A. Sloane, Dec 24 2012

Ruslan Sharipov, Asymptotic estimates for roots of the cuboid characteristic equation in the linear region, arXiv preprint, 2015.

Ruslan Sharipov, Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture, arXiv preprint, 2015.

Ruslan Sharipov, A note on invertible quadratic transformations of the real plane, arXiv preprint arXiv:1507.01861, 2015

Eric Weisstein's World of Mathematics, Euler Brick

Index entries for sequences related to bricks

Crossrefs

Cf. A031173, A031174.

Sequence in context: A233949 A233942 A122245 * A098826 A160284 A060836

Adjacent sequences: A031172 A031173 A031174 * A031176 A031177 A031178

Keyword

nonn

Author

Eric W. Weisstein

Status

approved