A071713 a(n) = smallest value of |x^n + y^n + z^n| for x,y,z distinct nonzero integers.

0, 14, 1, 98

Offset

1,2

Comments

If n is even, a(n)=1+2^n+3^n. Does a(5)=12 ?

The conjectured minimum of 12 for a(5) can be achieved by (x,y,z) = (13,16,-17). - Stefan Steinerberger, Dec 13 2007

Not only must x,y,z, be distinct, but also |x|, |y|, |z|. Otherwise take x = -y and z = 1; then for any odd n, a(n) = |x^n + (-x)^n + 1^n| = 1. - Ryan Propper, Feb 06 2008

Links

Table of n, a(n) for n=1..4.

K. S. Brown, A Conjecture on the Fermat Function (in Marginalia)

Crossrefs

Sequence in context: A040208 A097181 A040209 * A147716 A223516 A350888

Adjacent sequences: A071710 A071711 A071712 * A071714 A071715 A071716

Keyword

more,nonn,hard

Author

Benoit Cloitre, Jun 03 2002

Status

approved